Interferometer and method for measuring the refractive index and optical path length effects of air

ABSTRACT

Apparatus and methods particularly suitable for use in electro-optical metrology and other applications to measure and monitor the refractive index of a gas in a measurement path and/or the change in optical path length of the measurement path due to the gas while the refractive index of the gas may be fluctuating due to turbulence or the like and/or the physical length of the measuring path may be changing. More specifically, the invention employs electronic frequency processing to provide measurements of dispersion of the refractive index, the dispersion being substantially proportional to the density of the gas, and/or measurements of dispersion of the optical path length, the dispersion of the optical path length being related to the dispersion of the refractive index and the physical length of the measurement path. The refractive index of the gas and/or the optical path length effects of the gas are subsequently computed from the measured dispersion of the refractive index and/or the measured dispersion of the optical path length, respectively. The information generated by the inventive apparatus is particularly suitable for use in interferometric distance measuring instruments (DMI) to compensate for errors related to refractive index of gas in a measurement path brought about by environmental effects and turbulence induced by rapid stage slew rates.

CROSS REFERENCE TO RELATED APPLICATIONS

This application is a divisional U.S. patent application Ser. No.09/252,266 now U.S. Pat. No. 6,327,039, filed on Feb. 18, 1999, which,in turn, claims priority from U.S. Provisional Application No.60/075,586 filed on Feb. 23, 1998 and entitled “INTERFEROMETER ANDMETHOD FOR MEASURING THE REFRACTIVE INDEX AND OPTICAL PATH LENGTHEFFECTS OF AIR” and is a continuation-in-part of U.S. patent applicationSer. No. 09/078,254 filed on May 13, 1998, now abandoned and entitled“INTERFEROMETRIC APPARATUS AND METHODS USING ELECTRONIC FREQUENCYPROCESSING FOR MEASURING AND COMPENSATING FOR REFRACTIVE INDEX EFFECTSIN AN OPTICAL PATH”. Both of said applications are commonly ownedherewith, and their contents are incorporated herein by reference. Thisapplication is also related to commonly owned U.S. Pat. No. 5,838,485.

FIELD OF THE INVENTION

The present invention relates to optical instruments for measuringdistance and refractive index. The invention relates in particular tointerferometric distance measurement independent of the optical pathlength effects of refractive index of gas in a measurement pathincluding the effects of refractive index fluctuations.

BACKGROUND AND PRIOR ART

A frequently-encountered problem in metrology is the measurement of therefractive index of a column of air. Several techniques exist formeasuring the index under highly controlled circumstances, such as whenthe air column is contained in a sample cell and is monitored fortemperature, pressure, and physical dimension. See for example, anarticle entitled “An air refractometer for interference lengthmetrology,” by J. Terrien, Metrologia 1(3), 80-83 (1965).

Perhaps the most difficult measurement related to the refractive indexof air is the measurement of refractive index fluctuations over ameasurement path of unknown or variable length, with uncontrolledtemperature and pressure. Such circumstances arise frequently ingeophysical and meteorological surveying, for which the atmosphere isobviously uncontrolled and the refractive index is changing dramaticallybecause of variations in air density and composition. The problem isdescribed in an article entitled “Effects of the atmospheric phasefluctuation on long-distance measurement,” by H. Matsumoto and K.Tsukahara, Appl. Opt. 23(19), 3388-3394 (1984), and in an articleentitled “Optical path length fluctuation in the atmosphere,” by G. N.Gibson et al., Appl. Opt. 23(23), 4383-4389 (1984).

Another example situation is high-precision distance measuringinterferometry, such as is employed in micro-lithographic fabrication ofintegrated circuits. See for example an article entitled “Residualerrors in laser interferometry from air turbulence and nonlinearity,” byN. Bobroff, Appl. Opt. 26(13), 2676-2682 (1987), and an article entitled“Recent advances in displacement measuring interferometry,” also by N.Bobroff, Measurement Science & Tech. 4(9), 907-926 (1993). As noted inthe aforementioned cited references, interferometric displacementmeasurements in air are subject to environmental uncertainties,particularly to changes in air pressure and temperature; touncertainties in air composition such as resulting from changes inhumidity; and to the effects of turbulence in the air. Such factorsalter the wavelength of the light used to measure the displacement.Under normal conditions the refractive index of air is approximately1.0003 with a variation of the order of 1×10⁻⁵ to 1×10⁻⁴. In manyapplications the refractive index of air must be known with a relativeprecision of less than 0.1 ppm (parts per million) to 0.003 ppm, thesetwo relative precisions corresponding to a displacement measurementaccuracy of 100 nm and 3 nm, respectively, for a one meterinterferometric displacement measurement.

There are frequent references in the art to heterodyne methods of phaseestimation, in which the phase varies with time in a controlled way. Forexample, in a known form of prior-art heterodyne distance-measuringinterferometer, the source emits two orthogonally polarized beams havingslightly different optical frequencies (e.g. 2 MHz). The interferometricreceiver in this case is typically comprised of a linear polarizer and aphotodetector to measure a time-varying interference signal. The signaloscillates at the beat frequency and the phase of the signal correspondsto the relative phase difference. A further representative example ofthe prior art in heterodyne distance-measuring interferometry is taughtin commonly-owned U.S. Pat. No. 4,688,940 issued to G. E. Sommargren andM. Schaham (1987). However, these known forms of interferometricmetrology are limited by fluctuations in refractive index, and bythemselves are unsuited to the next generation of microlithographyinstruments.

Another known form of interferometer for distance measurement isdisclosed in U.S. Pat. No. 4,005,936 entitled “Interferometric MethodsAnd Apparatus For Measuring Distance To A Surface” issued to J. D.Redman and M. R. Wall (1977). The method taught by Redman and Wallconsists of employing laser beams of two different wavelengths, each ofwhich is split into two parts. Frequency shifts are introduced into onepart of the respective beams. One part of each beam reflects from anobject and recombines with the other part on a photodetector. From theinterference signal at the detector is derived a phase, at a differencefrequency, that is a measure of the distance to the surface. Theequivalent wavelength of the phase associated with the differencefrequency is equal to the product of the two laser wavelengths dividedby the difference of the two wavelengths. This two-wavelength techniqueof Redman and Wall reduces measurement ambiguities, but is at least assensitive to the deleterious effects of refractive index fluctuations ofthe air as single-wavelength techniques.

Another example of a two-wavelength interferometer similar to that ofRedman and Wall is disclosed in U.S. Pat. No. 4,907,886 entitled “MethodAnd Apparatus For Two-Wavelength Interferometry With Optical HeterodyneProcesses And Use For Position Or Range Finding,” issued to R. Dändlikerand W. Heerburgg (1990). This system is also described in an articleentitled “Two-Wavelength Laser Interferometry Using SuperheterodyneDetection,” by R. Dändliker, R. Thalmann, and D. Prongué, Opt. Let.13(5), 339-341 (1988), and in an article entitled “High-AccuracyDistance Measurements With Multiple-Wavelength Interferometry,” by R.Dändliker, K. Hug, J. Politch, and E. Zimmermann. The system ofDändliker et al., as taught in U.S. Pat. No. 4,907,886, employs laserbeams of two wavelengths, each of the beams comprising two polarizationcomponents separated in frequency by means of acousto-optic modulation.After passing these beams collinearly through a Michelsoninterferometer, the polarization components are mixed, resulting in aninterference signal, i.e. a heterodyne signal. In that the heterodynesignal has a different frequency for each of the two wavelengths, aso-called superheterodyne signal results therefrom having a frequencyequal to the difference in the heterodyne frequencies and a phaseassociated with an equivalent wavelength equal to the product of the twolaser wavelengths divided by the difference of the two wavelengths.According to U.S. Pat. No. 4,907,886 (cited above), the phase of thesuperheterodyne signal is assumed to be dependent only on the positionof a measurement object and the equivalent wavelength. Therefore, thissystem is also not designed to measure or compensate for thefluctuations in the refractive index of air.

Further examples of the two-wavelength superheterodyne techniquedeveloped by Redman and Wall and by Dändliker and Heerburgg (citedabove) are found in an article entitled “Two-wavelength doubleheterodyne interferometry using a matched grating technique,” by Z.Sodnik, E. Fischer, T. Ittner, and H. J. Tiziani, Appl. Opt. 30(22),3139-3144 (1991), and in an article entitled “Diode laser and fiberoptics for dual-wavelength heterodyne interferometry,” by S. Manhart andR. Maurer, SPIE 1319, 214-216 (1990). However, neither one of theseexamples addresses the problem of refractive index fluctuations.

It may be concluded from the foregoing that the prior art in heterodyneand superheterodyne interferometry does not provide a high speed methodand corresponding means for measuring and compensating the optical pathlength effects of air in a measuring path, particularly effects due tofluctuations in the refractive index of air. This deficiency in theprior art results in significant measurement uncertainty, thus seriouslyaffecting the precision of systems employing such interferometers asfound for example in micro-lithographic fabrication of integratedcircuits. Future interferometers will necessarily incorporate aninventive, new method and means for measuring and compensating afluctuating refractive index in a measurement path comprised of achanging physical length.

One way to detect refractive index fluctuations is to measure changes inpressure and temperature along a measurement path and calculate theeffect on the optical path length of the measurement path. Mathematicalequations for effecting this calculation are disclosed in an articleentitled “The Refractivity Of Air,” by F. E. Jones, J. Res. NBS 86(1),27-32 (1981). An implementation of the technique is described in anarticle entitled “High-Accuracy Displacement Interferometry In Air,” byW. T. Estler, Appl. Opt. 24(6), 808-815 (1985). Unfortunately, thistechnique provides only approximate values, is cumbersome, and correctsonly for slow, global fluctuations in air density.

Another, more direct way to detect the effects of a fluctuatingrefractive index over a measurement path is by multiple-wavelengthdistance measurement. The basic principle may be understood as follows.Interferometers and laser radar measure the optical path length betweena reference and an object, most often in open air. The optical pathlength is the integrated product of the refractive index and thephysical path traversed by a measurement beam. In that the refractiveindex varies with wavelength, but the physical path is independent ofwavelength, it is generally possible to determine the physical pathlength from the optical path length, particularly the contributions offluctuations in refractive index, provided that the instrument employsat least two wavelengths. The variation of refractive index withwavelength is known in the art as dispersion, therefore this techniquewill be referred to hereinafter as the dispersion technique.

The dispersion technique for refractive index measurement has a longhistory, and predates the introduction of the laser. An article entitled“Long-Path Interferometry Through An Uncontrolled Atmosphere,” by K. E.Erickson, JOSA 52(7), 781-787 (1962), describes the basic principles andprovides an analysis of the feasibility of the technique for geophysicalmeasurements. Additional theoretical proposals are found in an articleentitled “Correction Of Optical Distance Measurements For TheFluctuating Atmospheric Index Of Refraction,” by P. L. Bender and J. C.Owens, J. Geo. Res. 70(10), 2461-2462 (1965).

Commercial distance-measuring laser radar based on the dispersiontechnique for refractive index compensation appeared in the 1970's. Anarticle entitled “Two-Laser Optical Distance-Measuring Instrument ThatCorrects For The Atmospheric Index Of Refraction,” by K. B. Earnshaw andE. N. Hernandez, Appl. Opt. 11(4), 749-754 (1972), discloses aninstrument employing microwave-modulated HeNe and HeCd lasers foroperation over a 5 to 10 km measurement path. Further details of thisinstrument are found in an article entitled “Field Tests Of A Two-Laser(4416A and 6328A) Optical Distance-Measuring Instrument Correcting ForThe Atmospheric Index Of Refraction,” by E. N. Hernandez and K. B.Earnshaw, J. Geo. Res. 77(35), 6994-6998 (1972). Further examples ofapplications of the dispersion technique are discussed in an articleentitled “Distance Corrections For Single- And Dual-Color Lasers By RayTracing,” by E. Berg and J. A. Carter, J. Geo. Res. 85(B11), 6513-6520(1980), and in an article entitled “A Multi-WavelengthDistance-Measuring Instrument For Geophysical Experiments,” by L. E.Slater and G. R. Huggett, J. Geo. Res. 81(35), 6299-6306 (1976).

Although instrumentation for geophysical measurements typically employsintensity-modulation laser radar, it is understood in the art thatoptical interference phase detection is more advantageous for shorterdistances. In U.S. Pat. No. 3,647,302 issued in 1972 to R. B. Zipin andJ. T. Zalusky, entitled “Apparatus For And Method Of Obtaining PrecisionDimensional Measurements,” there is disclosed an interferometricdisplacement-measuring system employing multiple wavelengths tocompensate for variations in ambient conditions such as temperature,pressure, and humidity. The instrument is specifically designed foroperation with a movable object, that is, with a variable physical pathlength. However, the phase-detection means of Zipin and Zalusky isinsufficiently accurate for high-precision measurement.

A more modern and detailed example is the system described in an articleby Y. Zhu, H. Matsumoto, T. O'ishi, SPIE 1319, Optics in ComplexSystems, 538-539 (1990), entitled “Long-Arm Two-Color Interferometer ForMeasuring The Change Of Air Refractive Index.” The system of Zhu et al.employs a 1064 nm wavelength YAG laser and an 632 nm HeNe laser togetherwith quadrature phase detection. Substantially the same instrument isdescribed in Japanese in an earlier article by Zhu et al. entitled“Measurement Of Atmospheric Phase And Intensity Turbulence For Long-PathDistance Interferometer,” Proc. 3^(rd) Meeting On Lightwave SensingTechnology, Appl. Phys. Soc. of Japan, 39 (1989). However, theinterferometer of Zhu et al. has insufficient resolution for allapplications, e.g. sub-micron interferometry for microlithography.

A recent attempt at high-precision interferometry for microlithographyis represented by U.S. Pat. No. 4,948,254 issued to A. Ishida (1990). Asimilar device is described by Ishida in an article entitled “TwoWavelength Displacement-Measuring Interferometer Using Second-HarmonicLight To Eliminate Air-Turbulence-Induced Errors,” Jpn. J. Appl. Phys.28(3), L473-475 (1989). In the article, a displacement-measuringinterferometer is disclosed which eliminates errors caused byfluctuations in the refractive index by means of two-wavelengthdispersion detection. An Ar⁺ laser source provides both wavelengthssimultaneously by means of a frequency-doubling crystal known in the artas BBO. The use of a BBO doubling crystal results in two wavelengthsthat are fundamentally phase locked, thus greatly improving thestability and accuracy of the refractive index measurement. However, thephase detection means, which employ simple homodyne quadraturedetection, are insufficient for high resolution phase measurement.Further, the phase detection and signal processing means are notsuitable for dynamic measurements, in which the motion of the objectresults in rapid variations in phase that are difficult to detectaccurately.

In U.S. Pat. No. 5,404,222 entitled “Interferometric Measuring SystemWith Air Turbulence Compensation,” issued to S. A. Lis (1995), there isdisclosed a two-wavelength interferometer employing the dispersiontechnique for detecting and compensating refractive index fluctuations.A similar device is described by Lis in an article entitled “An AirTurbulence Compensated Interferometer For IC Manufacturing,” SPIE 2440(1995). Improvement on U.S. Pat. No. 5,404,222 by S. A. Lis is disclosedin U.S. Pat. No. 5,537,209, issued July 1996. The principal innovationof this system with respect to that taught by Ishida in Jpn. J. Appl.Phys. (cited above) is the addition of a second BBO doubling crystal toimprove the precision of the phase detection means. The additional BBOcrystal makes it possible to optically interfere two beams havingwavelengths that are exactly a factor of two different. The resultantinterference has a phase that is directly dependent on the refractiveindex but is substantially independent of stage motion. However, thesystem taught by Lis has the disadvantage that it is complicated andrequires an additional BBO crystal for every measurement path. In thatmicrolithography stages frequently involve six or more measurementpaths, and that BBO can be relatively expensive, the additional crystalsare a significant cost burden. An additional disadvantage of Lis' systemis that it employs a low-speed (32-Hz) phase detection system based onthe physical displacement of a PZT transducer.

It is clear from the foregoing, that the prior art does not provide apractical, high-speed, high-precision method and corresponding means formeasuring refractive index of air and measuring and compensating for theoptical path length effects of the air in a measuring path, particularlythe effects due to fluctuations in the refractive index of the air. Thelimitations in the prior art arise principally from the followingunresolved technical difficulties: (1) Prior-art heterodyne andsuperheterodyne interferometers are limited in accuracy by fluctuationsin the refractive index of air; (2) Prior-art dispersion techniques formeasuring index fluctuations require extremely high accuracy ininterference phase measurement, typically exceeding by an order ofmagnitude the typical accuracy of high-precision distance-measuringinterferometers; (3) Obvious modifications to prior-art interferometersto improve phase-measuring accuracy would increase the measurement timeto an extent incompatible with the rapidity of stage motion in modernmicrolithography equipment; (4) Prior-art dispersion techniques requireat least two extremely stable laser sources, or a single source emittingmultiple, phase-locked wavelengths; (5) Prior-art dispersion techniquesin microlithography applications are sensitive to stage motion duringthe measurement, resulting in systematic errors; and (6) Prior-artdispersion techniques that employ doubling crystals (e.g. U.S. Pat. No.5,404,222 to Lis) as part of the detection system are expensive andcomplicated.

These deficiencies in the prior art have led to the absence of anypractical interferometric system for performing displacement measurementfor microlithography in the presence of a gas in a measurement pathwhere there are typically refractive index fluctuations and themeasurement path is comprised of a changing physical length.

Accordingly, it is an object of the invention to provide a method andapparatus for rapidly and accurately measuring and monitoring therefractive index of a gas in a measurement path and/or the optical pathlength effects of the gas wherein the refractive index may befluctuating and/or the physical length of the measurement path may bechanging.

It is another object of the invention to provide a method and apparatusfor rapidly and accurately measuring and monitoring the refractive indexof a gas in a measurement path and/or the optical path length effects ofthe gas wherein the accuracy of measurements and monitoring of therefractive index of the gas and/or of the optical path length effects ofthe gas are substantially not compromised by a rapid change in physicallength of measurement path.

It is another object of the invention to provide a method and apparatusfor rapidly and accurately measuring and monitoring the refractive indexof a gas in a measurement path and/or the optical path length effects ofthe gas wherein the method and apparatus does not require measurementand monitoring of environmental conditions such as temperature andpressure.

It is another object of the invention to provide a method and apparatusfor rapidly and accurately measuring and monitoring the refractive indexof a gas in a measurement path and/or the optical path length effects ofthe gas wherein the method and apparatus may use but does not requirethe use of two or more optical beams of differing wavelengths which arephase locked.

It is another object of the invention to provide a method and apparatusfor rapidly and accurately measuring and monitoring the optical pathlength effects of a gas in a measurement path wherein the lengths ofmeasuring paths in an interferometric measurement are substantially notused in a computation of the optical path length effects of the gas.

Other objects of the invention will, in part, be obvious and will, inpart, appear hereinafter. The invention accordingly comprises methodsand apparatus possessing the construction, steps, combination ofelements, and arrangement of parts exemplified in the detaileddescription to follow when read in connection with the drawings.

SUMMARY OF THE INVENTION

The present invention generally relates to apparatus and methods formeasuring and monitoring the refractive index of a gas in a measurementpath and/or the change in optical path length of the measurement pathdue to the gas wherein the refractive index of the gas may befluctuating, e.g., the gas is turbulent, and/or the physical length ofthe measuring path may be changing. The present invention also relatesto apparatus and methods for use in electro-optical metrology and otherapplications. More specifically, the invention operates to providemeasurements of dispersion of the refractive index, the dispersion beingsubstantially proportional to the density of the gas, and/ormeasurements of dispersion of the optical path length, the dispersion ofthe optical path length being related to the dispersion of therefractive index and the physical length of the measurement path. Therefractive index of the gas and/or the optical path length effects ofthe gas are subsequently computed from the measured dispersion of therefractive index and/or the measured dispersion of the optical pathlength, respectively. The information generated by the inventiveapparatus is particularly suitable for use in interferometric distancemeasuring instruments (DMI) to compensate for errors related torefractive index of gas in a measurement path brought about byenvironmental effects and turbulence induced by rapid stage slew rates.

Several embodiments of the invention have been made and these fallbroadly into two categories that address the need for more or lessprecision in final measurements. While the various embodiments sharecommon features, they differ in some details to achieve individualgoals.

In general, the inventive apparatus comprises interferometer meanshaving first and second measurement legs at least one of which changesin length and at least one of which is at least in part occupied by thegas. Perferably a reference leg and a measurement leg are used inpreferred embodiments. The constituent legs are preferably configuredand arranged so that the measurement leg has a portion of its opticalpath length substantially the same as the optical path length of thereference leg. The gas in the remaining portion of the optical path ofthe measurement leg in a typical interferometric DMI application is air.

Means for generating at least two light beams having differentwavelengths are included. In preferred embodiments, a source generates aset of light beams, the set of light beams being comprised of at leasttwo light beams, each beam of the set of light beams having a differentwavelength. The relationship between the wavelengths of the beams of theset of light beams, the approximate relationship, is known.

A set of frequency-shifted light beams is generated from the set oflight beams by introducing a frequency difference between twoorthogonally polarized components of each beam of the set of light beamssuch that no two beams of the set of frequency-shifted light beams havethe same frequency difference. For a given embodiment, the ratios of thewavelengths are the same as the known approximate relationship torelative precisions which depend on chosen operating wavelenghs and thecorresponding known approximate relationship. Because of this wavelengthdependence, these relative precisions are referred to as the respectiverelative precisions of the ratios of the wavelengths. In a number ofembodiments, the respective relative precisions of the ratios of thewavelengths are of an order of magnitude less than the respectivedispersions of the gas times the relative precision required for themeasurement of the respective refractive indices of the gas and/or forthe measurement of the respective changes in the optical path length ofthe measurement leg due to the gas.

In certain ones of the embodiments, the approximate relationship isexpressed as a sequence of ratios, each ratio comprising a ratio of loworder non-zero integers, e.g., 2/1, to respective relative precisions,the respective relative precisions of the sequence of ratios, wherein arespective relative precision of the respective relative precisions ofthe sequence of ratios is of an order of magnitude less than therespective dispersion of the gas times the respective relative precisionrequired for the measurement of the respective refractive index of thegas and/or for the measurement of the respective change in the opticalpath length of the measurement leg due to the gas.

In other embodiments, where the respective relative precisions of theratios of the wavelengths is inappropriate to the desired value, meansare provided for monitoring the ratios of the wavelengths and eitherproviding feedback to control the respective relative precisions of theratios of the wavelengths, information to correct subsequentcalculations influenced by undesirable departures of the respectiverelative precisions of the ratios of the wavelengths from the desiredrespective relative precisions of the ratios of the wavelengths, or somecombination of both. Means are also provided for monitoring thewavelength used in the primary objective of DMI, the determination of achange in a length of the measurement path.

At least a portion of each of the frequency-shifted light beams isintroduced into the interferometer means by suitable optical means sothat a first portion of at least a portion of each frequency-shiftedlight beam travels through the reference leg along predetermined pathsof the reference leg and a second portion of at least a portion of eachfrequency-shifted light beam travels through the measurement leg alongpredetermined paths of the measurement leg, the first and secondportions of at least a portion of each frequency-shifted light beambeing different. Afterwards, the first and second portions of at least aportion of each frequency-shifted light beam emerge from theinterferometer means as exit beams containing information about theoptical path length through the predetermined paths in the reference legand the optical path length through the predetermined paths in themeasurement leg.

Combining means are provided for receiving the exit beams to producemixed optical signals which contain information corresponding to thephase differences between the exit beams of the first and secondportions of at least a portion of each frequency-shifted light beam. Themixed optical signals are then sensed by a photodetector, preferably byphotoelectric detection, which operates to generate electricalinterference signals that contain information corresponding to therefractive index of the gas at the different beam wavelengths and to theoptical path length in the measurement leg due to the refractive indexof the gas at the different beam wavelengths.

In certain of the embodiments, modified electrical interference signalsare then generated from the electrical interference signals by eithermultiplying or dividing the phase of each of the electrical interferencesignals by a number, the relationship of the numbers being either thesame as the known approximate relationship of the wavelengths or thesame as the reciprocal of the known approximate relationship of thewavelengths, respectively.

The electrical interference signals, or the corresponding modifiedelectrical interference signals depending on the embodiment, are thenanalyzed by electronic means that operate to determine the dispersion ofthe optical path length of the measurement leg substantially due to thedispersion of the refractive index of the gas and/or the dispersion(n_(i)−n_(j)) of the gas where i and j are integers corresponding towavelengths and different from one another. From this information andthe reciprocal dispersive power of the gas, the refractivity of the gas,(n_(r)−1) where r is an integer corresponding to a wavelength, and/orthe contribution to the optical path length of the measurement leg dueto the refractive index of the gas can also be determined by theelectronic means. The value of r may be different from i and j or equalto either i or j. The electronic means can comprise electronic means inthe form of a microprocessor or a general purpose computer suitablyprogrammed in well-known ways to perform the needed calculations.

In preferred form, the electrical interference signals compriseheterodyne signals containing phase information corresponding to therefractive index of the gas and to the optical path length of themeasurement leg and the apparatus further comprises means to determinethe phases of the heterodyne signals to generate phase informationcorresponding to the dispersion of the refractive index of the gas andto the dispersion of the optical path length of the measurement leg dueto the dispersion of the refractive index of the gas. In certain of theembodiments, the apparatus further comprises means for mixing, i.e.multiplying, the modified heterodyne signals corresponding to themodified electrical signals to generate at least one modifiedsuperheterodyne signal containing phase corresponding to the dispersionof the refractive index of the gas and to the dispersion of the opticalpath length of the measurement leg due to the dispersion of therefractive index of the gas. Means are also included for resolving phaseambiguities of the heterodyne signals, modified heterodyne signals, andthe modified superheterodyne signals generated in certain of theembodiments. Depending on the details of the optical paths experiencedby the light beam portions as they travel through the interferometermeans of the various embodiments, additional or different electronicsare provided.

While the inventive method disclosed may be carried out using thepreferred apparatus described, it will be evident that it may also bepracticed using other well-known apparatus. In addition, it is shownthat apparatus may be employed which uses homodyne signals.

BRIEF DESCRIPTION OF THE DRAWINGS

The structure and operation of the invention, together with otherobjects and advantages thereof, may best be understood by reading thedetailed description in conjunction with the drawings wherein theinvention's parts have an assigned reference numeral that is used toidentify them in all of the drawings in which they appear and wherein:

FIGS. 1a-1 b taken together illustrate, in diagrammatic form, thepresently first preferred embodiment of the present invention with FIG.1a showing optical paths between indicated elements source 1, modulator3, source 2, modulator 4, interferometer 260, detectors 85 and 86, andtranslator 267 and the paths of electrical signals between indicatedelements driver 5, modulator 3, driver 6, modulator 4, detectors 85 and86, electronic processor 109, and computer 110;

FIG. 1b is a drawing showing a block diagram of the processingelectronics 109;

FIG. 1c is a drawing showing a block diagram of the processingelectronics 109A for the first variant of the first embodiment;

FIG. 1d is a drawing showing a block diagram of the processingelectronics 109B for the third variant of the first embodiment;

FIGS. 2a-2 f taken together illustrate, in diagrammatic form, thepresently second preferred embodiment of the present invention with FIG.2a showing optical paths between indicated elements source 1, modulator3, source 2, modulator 4, differential plane mirror interferometers 69and 70, beam splitter 65, external mirror system 90, detectors 185 and186, and translator 67 and the paths of electrical signals betweenindicated elements driver 5, modulator 3, driver 6, modulator 4,detectors 185 and 186, electronic processor 209, and computer 110;

FIG. 2b illustrates differential plane mirror interferometer 69;

FIG. 2c illustrates differential plane mirror interferometer 70;

FIG. 2d illustrates external mirror system 90, furnishing the externalmirrors for differential plane mirror interferometer 69, and stagetranslator 67;

FIG. 2e illustrates external mirror system 90, furnishing the externalmirrors for differential plane mirror interferometer 70, and stagetranslator 67;

FIG. 2f is a drawing showing a block diagram of the processingelectronics 209;

FIGS. 3a-3 b taken together illustrate, in diagrammatic form, thepresently preferred third embodiment of the present invention with FIG.3a showing optical paths and electronic paths of apparatus fordetermination of refractive index of a gas and/or the optical pathlength effects of the gas comprised in part of the same apparatus as forthe first preferred embodiment and optical paths and electronic paths ofapparatus for determination of χ and the ratio K/χ, a number of elementsof the apparatus for determination of χ and the ratio K/χ performinganalogous operations as apparatus of the first preferred embodimentapart from the suffix “b” when referring to apparatus for determinationof χ and the ratio K/χ;

FIG. 3b is a drawing showing a block diagram of the processingelectronics 109 b;

FIGS. 4a-4 c taken together illustrate, in diagrammatic form, thepresently preferred fourth embodiment of the present invention with FIG.4a showing optical paths and electronic paths of apparatus fordetermination of refractive index of a gas and/or the optical pathlength effects of the gas comprised in part of the same apparatus as forthe second preferred embodiment and optical paths and electronic pathsof apparatus for determination of the χ and ratio K/χ, a number ofelements of the apparatus for determination of χ and the ratio K/χperforming analogous operations as apparatus of the second preferredembodiment apart from the suffix “b” when referring to apparatus fordetermination of χ and the ratio K/χ;

FIG. 4b illustrates the external mirror system 90 b furnishing theexternal mirrors for differential plane mirror interferometer 69 b;

FIG. 4c illustrates the external mirror system 90 b furnishing theexternal mirrors for differential plane mirror interferometer 70 b;

FIG. 5 is a high-level flowchart depicting various steps carried out inpracticing a method in accordance with the invention;

FIGS. 6a-6 c relate to lithography and its application to manufacturingintegrated circuits wherein FIG. 6a is a schematic drawing of alithography exposure system employing the interferometry system.

FIGS. 6b and 6 c are flow charts describing steps in manufacturingintegrated circuits; and

FIG. 7 is a schematic of a beam writing system employing theinterferometry system.

DETAILED DESCRIPTION OF THE INVENTION

The present invention relates to apparatus and methods by which therefractivity of a gas in at least one measurement path and/or the changein the optical path length of the measurement path due to the gas may bequickly measured and used in subsequent downstream or contemporaneousapplications wherein either or both the refractive index of the gas andthe physical length of the measurement path may be changing. An exampleof a contemporaneous application is in an interferometric distancemeasuring instrument to enhance accuracy by compensating for the effectsof the refractive index of the gas in the measurement path, especiallychanges in the optical path length that take place during the measuringperiod because of changing environmental conditions or air turbulenceinduced in the measurement path by rapid stage slew rates.

A number of different embodiments of the apparatus of the invention areshown and described. While they differ in some details, the disclosedembodiments otherwise share many common elements and naturally fall intotwo categories depending on the degree of control demanded of theirlight sources. As will be seen, the disclosed embodiments within eachcategory also differ in the details of how their interferometric opticalpaths are implemented and/or how certain information signals are handledelectronically.

The first group of embodiments to be described comprise two embodimentsand variants thereof. This group is intended for applications where thestability of the adopted light sources is sufficient and the ratio ofthe wavelengths of the light beams generated by the adopted lightsources is matched to a sequence of known ratio values with respectiverelative precisions sufficient to meet the required precision imposed onthe output data by the final end use application.

The second group of embodiments also comprise two embodiments andvariants thereof and these are particularly suitable for use where it isnecessary to monitor the stability of the light sources and measure theratios of the wavelengths of the light beams generated by the adoptedlight sources to meet performance requirements on accuracy. For bothgroups, apparatus is disclosed for dealing with phase ambiguities andphase and group delays that may arise in analyzing homodyne, heterodyne,and/or superheterodyne signals and methods are disclosed forimplementing the steps of the invention.

FIGS. 1a and 1 b depict in schematic form one preferred embodiment ofthe present invention for measuring and monitoring the refractivity of agas in a measurement path and/or the change in the optical path lengthof the measurement path due to the gas wherein either or both therefractive index of the gas and the physical length of the measurementpath may be changing and where the stability of the adopted lightsources is sufficient and the ratio of the wavelengths of the lightbeams generated by the adopted light sources is matched to a known ratiovalue with a relative precision sufficient to meet the requiredprecision imposed on the output data by the final end use application.While the apparatus has application for a wide range of radiationsources, the following description is taken by way of example withrespect to an optical measuring system.

Referring to FIG. 1a and in accordance with the preferred apparatus andmethod of the first preferred embodiment of the present invention, alight beam 7 emitted from source 1 passes through a modulator 3 becominglight beam 9. Modulator 3 is excited by a driver 5. Source 1 ispreferably a laser or like source of coherent radiation, preferablypolarized, and having a wavelength λ₁. Modulator 3 may for example be anacousto-optical device or a combination of acousto-optical devices withadditional optics for selectively modulating polarization components ofbeam 7. Modulator 3 preferably shifts the oscillation frequency of onelinearly polarized component of beam 7 an amount f₁ with respect to anorthogonally linearly polarized component, the directions ofpolarizations of the components denoted herein as x and y. In thefollowing description of the first preferred embodiment, it will beassumed that the x polarization component of beam 9 has an oscillationfrequency shifted an amount f₁ with respect to the y polarizationcomponent of beam 9 without departing from the spirit or scope of thepresent invention. The oscillation frequency f₁ is determined by thedriver 5.

In a next step, a light beam 8 emitted from a source 2 passes through amodulator 4 becoming light beam 10. Modulator 4 is excited by a driver6, similar to modulator 3 and driver 5, respectively. Source 2, similarto source 1, is preferably a laser or like source of polarized, coherentradiation, but preferably at a different wavelength, λ₂, wherein theratio of the wavelengths (λ₁/λ₂) has a known approximate ratio valuel₁/l₂ , i.e.

(λ₁/λ₂)≅(l ₁ /l ₂),  (1)

where l₁ and l₂ may assume integer and non-integer values, and the ratioof the wavelengths (λ₁/λ₂) is the same as the ratio value l₁/l₂ to arelative precision of an order of magnitude or more less than thedispersion of the refractive index of the gas, (n₂−n₁), times therelative precision ε desired for the measurement of the refractivity ofthe gas or of the change in the optical path length of the measurementleg due to the gas. The x polarized component of beam 10 has anoscillation frequency shifted an amount f₂ with respect to the ypolarized component of beam 10. The oscillation frequency f₂ isdetermined by the driver 6. In addition, the directions of the frequencyshifts of the x components of beams 9 and 10 are the same.

It will be appreciated by those skilled in the art that beams 7 and 8may be provided alternatively by a single laser source emitting morethan one wavelength, by a single laser source combined with opticalfrequency doubling means to achieve frequency doubling, tripling,quadrupling, etc., two laser sources of differing wavelengths combinedwith sum-frequency generation or difference-frequency generation, or anyequivalent source configuration capable of generating light beams of twoor more wavelengths.

A laser source, for example, can be a gas laser, e.g. a HeNe, stabilizedin any of a variety of conventional techniques known to those skilled inthe art, see for example, T. Baer et al., “Frequency Stabilization of a0.633 μm He—Ne-longitudinal Zeeman Laser,” Applied Optics, 19, 3173-3177(1980); Burgwald et al., U.S. Pat. No. 3,889,207, issued Jun. 10, 1975;and Sandstrom et al., U.S. Pat. No. 3,662,279, issued May 9, 1972.Alternatively, the laser can be a diode laser frequency stabilized inone of a variety of conventional techniques known to those skilled inthe art, see for example, T. Okoshi and K. Kikuchi, “FrequencyStabilization of Semiconductor Lasers for Heterodyne-type OpticalCommunication Systems,” Electronic Letters, 16, 179-181 (1980) and S.Yamaqguchi and M. Suzuki, “Simultaneous Stabilization of the Frequencyand Power of an AlGaAs Semiconductor Laser by Use of the OptogalvanicEffect of Krypton,” IEEE J. Quantum Electronics, QE-19, 1514-1519(1983).

It will also be appreciated by those skilled in the art that the twooptical frequencies of beam 9 and of beam 10 may be produced by any of avariety of frequency modulation apparatus and/or lasers: (1) use of aZeeman split laser, see for example, Bagley et al., U.S. Pat. No.3,458,259, issued Jul. 29, 1969; G. Bouwhuis, “Interferometrie MitGaslasers,” Ned. T. Natuurk, 34, 225-232 (August 1968); Bagley et al.,U.S. Pat. No. 3,656,853, issued Apr. 18, 1972; and H. Matsumoto, “Recentinterferometric measurements using stabilized lasers,” PrecisionEngineering, 6(2), 87-94 (1984); (2) use of a pair of acousto-opticalBragg cells, see for example, Y. Ohtsuka and K. Itoh, “Two-frequencyLaser Interferometer for Small Displacement Measurements in a LowFrequency Range,” Applied Optics, 18(2), 219-224 (1979); N. Massie etal., “Measuring Laser Flow Fields With a 64-Channel HeterodyneInterferometer,” Applied Optics, 22(14), 2141-2151 (1983); Y. Ohtsukaand M. Tsubokawa, “Dynamic Two-frequency Interferometry for SmallDisplacement Measurements,” Optics and Laser Technology, 16, 25-29(1984); H. Matsumoto, ibid.; P. Dirksen, et al., U.S. Pat. No.5,485,272, issued Jan. 16, 1996; N. A. Riza and M. M. K. Howlader,“Acousto-optic system for the generation and control of tunablelow-frequency signals,” Opt. Eng., 35(4), 920-925 (1996); (3) use of asingle acousto-optic Bragg cell, see for example, G. E. Sommargren,commonly owned U.S. Pat. No. 4,684,828, issued Aug. 4, 1987; G. E.Sommargren, commonly owned U.S. Pat. No. 4,687,958, issued Aug. 18,1987; P. Dirksen, et al., ibid.; (4) use of two longitudinal modes of arandomly polarized HeNe laser, see for example, J. B. Ferguson and R. H.Morris, “Single Mode Collapse in 6328 Å HeNe Lasers,” Applied Optics,17(18), 2924-2929 (1978); or (5) use of birefringent elements or thelike internal to the laser, see for example, V. Evtuhov and A. E.Siegman, “A ‘Twisted-Mode’ Technique for Obtaining Axially UniformEnergy Density in a Laser Cavity,” Applied Optics, 4(1), 142-143 (1965).

The specific device used for the sources of beams 7 and 8 will determinethe diameter and divergence of beams 7 and 8, respectively. For somesources, e.g., a diode laser, it will likely be necessary to useconventional beam shaping optics, e.g., a conventional microscopeobjective, to provide beams 7 and 8 with a suitable diameter anddivergence for the elements that follow. When the source is a HeNelaser, for example, beam shaping optics may not be required.

It will be further appreciated by those skilled in the art that both thex and y polarization components of beam 9 and/or of beam 10 may befrequency shifted without departing from the scope and spirit of theinvention, f₁ remaining the difference in frequencies of the x and ypolarization components of beam 9 and f₂ remaining the difference infrequencies of the x and y polarization components of beam 10. Improvedisolation of an interferometer and a laser source is generally possibleby frequency shifting both x and y polarization components of a beam,the degree of improved isolation depending on the means used forgenerating the frequency shifts.

In a next step, beam 9 is reflected by mirror 253A and then a portion ofbeam 9 is subsequently reflected by beamsplitter 253B, preferably anon-polarizing type, to become a component of beam 213, the λ₁component. A portion of beam 10 is transmitted by beamsplitter 253B tobecome a second component of beam 213, the λ₂ component, wherein the λ₂component is preferably parallel and coextensive with the λ₁ component.In a further step, beam 213 propagates to an interferometer 260,comprised of optical means for a introducing a phase shift ψ₁ betweenthe polarization components x and y of the λ₁ component of beam 213 anda phase shift ψ₂ between the polarization components x and y of the λ₂component of beam 213. The magnitude of phase shifts ψ₁ and ψ₂ arerelated to round-trip physical length L of measurement path 298according to the formulae

ψ_(j) =Lpk _(j) n _(j)+ζ_(j) , j=1 and 2,  (2)

where p is the number of passes through the respective reference andmeasurement legs for a multiple pass interferometer, and n_(j) are therefractive indices of gas in measurement path 298 corresponding towavenumber k_(j)=(2π)/λ_(j) . The phase offsets ζ_(j) comprise allcontributions to the phase shifts ψ_(j) that are not related to themeasurement path 298 or reference paths.

As shown in FIG. 1a, interferometer 260 is comprised of a referenceretroreflector 295, object retroreflector 296, quarter-wave phaseretardation plates 221 and 222, and a polarizing beam splitter 223. Thisconfiguration is known in the art as a polarized Michelsoninterferometer, and is shown as a simple illustration with p=1.

Eqs. (2) are valid for the case where the paths for one wavelength andthe paths for the second wavelength are substantially coextensive, acase chosen to illustrate in the simplest manner the function of theinvention in the first embodiment. To those skilled in the art, thegeneralization to the case where the respective paths for the twodifferent wavelengths are not substantially coextensive is a straightforward procedure.

Cyclic errors that produce nonlinearities in distance measuringinterferometry (cf. the cited articles by Bobroff) have been omitted inEqs. (2). Techniques known to those skilled in the art can be used toeither reduce the cyclic errors to negligible levels or compensate forthe presence of cyclic errors, techniques such as using separated beamsin the interferometer and/or separated beams in the delivery system forlight beams from each light beam source to the interferometer [M.Tanaka, T. Yamagami, and K. Nakayama, “Linear Interpolation of PeriodicError in a Heterodyne Laser Interferometer at Subnanometer Levels,” IEEETrans. Instrum. and Meas., 38(2), 552-554, 1989] and light beam sourceswith reduced polarization and/or frequency mixing.

After passing through interferometer 260, beam 213 becomes aphase-shifted beam 215, which passes through a polarizer 244 preferablyorientated so as to mix polarization components x and y of beam 215. Aconventional dichroic beam splitter 280 preferably separates thoseportions of beam 215 corresponding to wavelengths λ₁ and λ₂ into beams217 and 218, respectively.

In a next step as shown in FIG. 1a, phase-shifted beams 217 and 218impinge upon photodetectors 85 and 86, respectively, resulting in twoelectrical interference signals, heterodyne signals s₁ and s₂,respectively, preferably by photoelectric detection. The signal s₁corresponds to wavelength λ₁ and signal s₂ corresponds to the wavelengthλ₂. The signals s_(j) have the form

 s _(j) =A _(j) cos[α_(j)(t)], j=1 and 2,  (3)

where the time-dependent arguments α_(j)(t) are given by

α_(j)(t)=2πf _(j) t+ψ _(j) , j=1 and 2  (4)

Heterodyne signals s₁ and s₂ are transmitted to electronic processor 109for analysis as electronic signals 103 and 104, respectively, in eitherdigital or analog format, preferably in digital format.

A preferred method for electronically processing the heterodyne signalss₁ and s₂ is presented herewithin for the case when l₁ and/or l₂ are notlow order integers. For the case when l₁ and l₂ are both low orderintegers and the ratio of the wavelengths matched to the ratio (l₁/l₂)with a relative precision sufficient to meet the required precisionimposed on the output data by the end use application, the preferredprocedure for electronically processing the heterodyne signals s₁ and s₂is the same as the one subsequently set down for the second variant ofthe first preferred embodiment of the present invention.

Referring now to FIG. 1b, electronic processor 109 further compriseselectronic processors 1094A and 1094B to determine the phases ψ₁ and ψ₂,respectively, by either digital or analog signal processes, preferablydigital processes, using time-based phase detection such as a digitalHilbert transform phase detector [see section 4.1.1 of “Phase-lockedloops: theory, design, and applications” 2nd ed. McGraw-Hill (New York)1993, by R. E. Best] or the like and the phase of drivers 5 and 6.

The phases of drivers 5 and 6 are transmitted by electrical signals,reference signals 101 and 102, respectively, in either digital or analogformat, preferably in digital format, to electronic processor 109.Reference signals, alternatives to reference signals 101 and 102, mayalso be generated by an optical pick off means and detectors (not shownin figures) by splitting off portions of beams 9 and 10 with beamsplitters, preferably non-polarizing beam splitters, mixing the portionof the beam 9 and the portion of the beam 10 that are split off, anddetecting the mixed portions to produce alternative heterodyne referencesignals.

Referring again to FIG. 1b, phase ψ₁ and phase ψ₂ are next multiplied byλ₁/p and λ₂/p respectively, in electronic processors 1095A and 1095B,respectively, preferably by digital processing, resulting in phases(l₁/p)ψ₁ and (l₂/p)ψ₂, respectively. The phases (l₁/p)ψ₁ and (l₂/p)ψ₂are next added together in electronic processor 1096A and subtracted onefrom the other in electronic processor 1097A, preferably by digitalprocesses, to create the phases θ and Φ, respectively. Formally,$\begin{matrix}{{\vartheta = ( {{\frac{l_{1}}{p}\phi_{1}} + {\frac{l_{2}}{p}\phi_{2}}} )},} & (5) \\{\Phi = {( {{\frac{l_{1}}{p}\phi_{1}} - {\frac{l_{2}}{p}\phi_{2}}} ).}} & (6)\end{matrix}$

The phases ψ₁, θ, and Φ are transmitted to computer 110 as signal 105,in either digital or analog format, preferably in digital format.

For a measuring path comprised of a vacuum, phase Φ should substantiallybe a constant independent of Doppler shifts due to a motion ofretroreflector 296. This may not be the case in practice due todifferences in the group delay experienced by the electrical signals s₁and s₂. Group delay, often called envelope delay, describes the delay ofa packet of frequencies, and the group delay at a particular frequencyis defined as the negative of the slope of the phase curve at theparticular frequency [see H. J. Blinchikoff and A. I. Zverev, Filteringin the Time and Frequency Domains, Section 2.6, 1976 (Wiley, N.Y.)]. Ifphase Φ is not a constant for a measuring path comprised of a vacuum,techniques known to those skilled in the art can be used to compensatefor departures of phase Φ from a constant (cf. Blinchikoff and Zveriv,ibid.) . It is important to note that the group delay effects in Φ cannot only be detected but can also be determined by measuring Φ as afunction of different translational velocities of retroreflector 296produced by translator 267 for a measuring path comprising a vacuum. Itis also important to note that the group delay effects in Φ can besignificantly reduced by performing analog-to-digital conversion ofsignals s₁ and s₂ as close as practical to the photoelectric detectorsin detectors 85 and 86, respectively, followed by digital signalprocessing as opposed to transmitting the signals s₁ and s₂ as analogsignals for subsequent analog signal processing and/or analog-to-digitalconversion downstream. The compensation for a particular group delay cangenerally be introduced before or after, or in part before and in partafter, the processing elements producing the particular group delay.

The refractivity of the gas, (n₁−1), can be calculated using the formula$\begin{matrix}{{{n_{1} - 1} = {\frac{\Gamma}{\chi \quad {L\lbrack {1 - ( {K/\chi} )^{2}} \rbrack}}\{ {\lbrack {{\vartheta ( {K/\chi} )} - \Phi} \rbrack - Q} \}}},} & (7)\end{matrix}$

where

χ=(l ₁ k ₁ +l ₂ k ₂)/2,  (8)

K=(l ₁ k ₁ −l ₂ k ₂)/2  (9)

and $\begin{matrix}{{\Gamma = \frac{n_{1} - 1}{n_{2} - n_{1}}},} & (10)\end{matrix}$

the quantity Γ being the reciprocal dispersive power of the gas which issubstantially independent of environmental conditions and turbulence inthe gas. The offset term Q is defined as

Q=ξ(K/χ)−Z  (11)

where $\begin{matrix}{{\xi = ( {{\frac{l_{1}}{p}\zeta_{1}} + {\frac{l_{2}}{p}\zeta_{2}}} )},} & (12) \\{Z = {( {{\frac{l_{1}}{p}\zeta_{1}} - {\frac{l_{2}}{p}\zeta_{2}}} ).}} & (13)\end{matrix}$

Values of Γ may be computed from knowledge of the gas composition andfrom knowledge of the wavelength dependent refractivities of the gasconstituents. For the example of λ₁=0.63 μm, λ₂=0.32 μm, and a standardatmosphere, Γ≅24.

In addition, Eq. (7) is valid for the case where the combined paths foroptical beams at one wavelength are substantially coextensive with thecombined paths for optical beams at a second wavelength, a preferredconfiguration that also serves to illustrate in the simplest manner thefunction of the invention. To those skilled in the art, thegeneralization to the case where combined paths for optical beams at onewavelength are not substantially coextensive with the combined paths foroptical beams at a second wavelength is a straight forward procedure.

For those applications related to distance measuring interferometry, theheterodyne phase ψ₁ and phases θ and Φ may be used to determine aphysical distance L, independent of the effects of the refractive indexof the gas in the measuring path of a distance measuring interferometer,using the formula $\begin{matrix}{L = {\frac{1}{( {\chi + K} )}{\{ {{\frac{l_{1}}{p}( {\phi_{1} - \zeta_{1}} )} - {\frac{\Gamma}{\lbrack {1 - ( {K/\chi} )} \rbrack}\lbrack {{( {K/\chi} )\vartheta} - \Phi - Q} \rbrack}} \}.}}} & (14)\end{matrix}$

The ratio of the wavelengths can be expressed in terms of (K/χ) fromEqs. (8) and (9) with the result $\begin{matrix}{\frac{\lambda_{1}}{\lambda_{2}} = {{( \frac{l_{1}}{l_{2}} )\lbrack \frac{1 - ( {K/\chi} )}{1 + ( {K/\chi} )} \rbrack}.}} & (15)\end{matrix}$

When operating under the condition $\begin{matrix}{{{{K/\chi}}\frac{( {n_{2} - n_{1}} )}{( {n_{2} + n_{1}} )}},} & (16)\end{matrix}$

the ratio of the phases Φ and θ has the approximate value$\begin{matrix}{( {\Phi/\vartheta} ) \cong {- {\frac{( {n_{2} - n_{1}} )}{( {n_{2} + n_{1}} )}.}}} & (17)\end{matrix}$

Therefore, for the case of the first preferred embodiment where theratio of the wavelengths (λ₁/λ₂) has a known approximate ratio valuel₁/l₂, cf. Eq. (1), where l₁ and l₂ may assume integer and non-integervalues, and the ratio of the wavelengths (λ₁/λ₂) is the same as theratio value l₁/l₂ to a relative precision of an order of magnitude ormore less than the dispersion of the refractive index of the gas,(n₂−n₁), times the relative precision ε desired for the measurement ofthe refractivity of the gas or of the change in the optical path lengthof the measurement leg due to the gas, expressed formally by theinequality $\begin{matrix}{{{{\frac{\lambda_{1}}{\lambda_{2}} - \frac{l_{1}}{l_{2}}}}{( \frac{l_{1}}{l_{2}} )( {n_{2} - n_{1}} )ɛ}},} & (18)\end{matrix}$

Eqs. (7) and (14) reduce to more simple forms of $\begin{matrix}{{{n_{1} - 1} = {{- \frac{\Gamma}{\chi \quad L}}( {\Phi + Q} )}},} & (19) \\{L = {\frac{1}{\chi}\lbrack {{{\frac{l_{1}}{p}( {\phi_{1} - \zeta_{1}} )} + {\Gamma ( {\Phi + Q} )}},} }} & (20)\end{matrix}$

respectively. It will also be obvious to someone skilled in the art toperform similar calculations for L with respect to n₂,

(n ₂−1)=(n ₁−1)(1+1/Γ),  (21)

in place of or in addition to n₁.

In a next step, electronic processing means 109 transmits to thecomputer 110 ψ₁ and Φ as electronic signal 105 in either digital oranalog format, preferably a digital format, for the computation of(n₁−1) and/or L. The resolution of phase redundancy in (1/l₁)Φ isrequired in the computation of either (n₁−1) or changes in L due to thegas using either Eqs. (19) or (20), respectively. In addition, theresolution of phase redundancy in ψ₁ is required in the computation of Lusing Eq., and the resolution of the phase redundancy in ψ₁ is requiredin the computation of changes L using Eq. (20) if χ is variable in time.

The equivalent wavelength comprising (1/l₁)Φ is significantly largerthan either of the wavelengths λ₁ and λ₂ and as a consequence, producesa significant simplification in a procedure implemented for resolutionof phase redundancy in (1/l₁)Φ. The equivalent wavelength λ_((1/l) ₁)_(Φ) for (1/l₁)Φ is $\begin{matrix}{\lambda_{{({1/t_{1}})}\Phi} = {\frac{\lambda_{1}}{( {n_{2} - n_{1}} )}.}} & (22)\end{matrix}$

For the example of λ₁=0.63 μm, λ₂=0.32 μm, and (n₂−n₁)≅1×10⁻⁵ for astandard atmosphere, the equivalent wavelength given by Eq. (22) is

λ _((1/l) ₁ )_(Φ)≅63 mm.  (23)

Any one of several procedures may be easily employed to resolve thephase redundancy in (1/l₁)Φ, given the equivalent wavelength asexpressed by Eq. (22). For those applications where changes in themeasurement path can be measured interferometrically, a feature forexample of an application based on a distance measuring interferometeremployed for measuring changes in the measurement path, the movableretroreflector 296 of interferometer 260 can be scanned by translator267 in a controlled manner over a given length and the concomitantchange in (1/l₁)Φ recorded. From the recorded change in (1/l₁)Φ and thelength scanned, as recorded by the change in ψ₁, the equivalentwavelength λ_((1/l) ₁ _()Φ) can be calculated. With the computed valuefor the equivalent wavelength λ_((1/l) ₁ _()Φ), the phase redundancy in(1/l₁)Φ can be easily resolved in view of the relatively large value forthe equivalent wavelength λ_((1/l) ₁ _()Φ).

For those applications where the determination of the refractivityand/or or the change in the optical path length due to the gas in ameasurement leg is made and retroreflector 296 does not have a scanningcapability such as considered in the preceding paragraph, otherprocedures are available for the resolution of the phase redundancy of(1/l₁)Φ. One procedure which may be employed to resolve the phaseredundancy in (1/l₁)Φ is based on the use of a retroreflector or seriesof retroreflectors inserted at a series of positions in measurement path298, the retroreflector at each position of the series of positionsperforming the same function as retroreflector 296, wherein theround-trip physical length L for the measurement leg for each positionof the series of positions of the inserted retroreflectors form ageometric progression. The smallest or first round-trip physical lengthin the series of positions will be approximately λ₁/[4(n₂−n₁)] dividedby the relative precision that the initial value of (1/l₁)Φ is known.The round-trip physical length of the second position of the series ofpositions will be approximately the round-trip physical length of thefirst position of the series of positions divided by the relativeprecision that Φ is measured using the first position of the series ofpositions. This is a geometric progression procedure, the resultingsequence of roundtrip physical lengths forming a geometric progression,which is continued until the round-trip physical length of theretroreflector 296 used to measure the refractivity or the change inoptical path length due to the refractivity of the gas would be exceededif the number of positions in the series of positions were incrementedby one.

A third procedure is based upon the use of a source not shown in FIGS.1a and 1 b) of a series of known wavelengths and measuring Φ for thesewavelengths. The number of known wavelengths required for the resolutionof the phase redundancy is generally comprised of a small set because ofthe relatively large value for λ_((1/l) ₁ _()Φ) as given by Eq. (22).

Another procedure to resolve the phase redundancy in (1/l₁)Φ would be toobserve the changes in (1/l₁)Φ as the measuring path 98 is changed frombeing filled with a gas to an evacuated state (the vacuum chamber andpump and requisite gas handling system are not shown in FIGS. 1a and 1b) to resolve the phase redundancy in (1/l₁)Φ. The problems normallyencountered in measuring absolute values for refractivity and changes inthe optical path length due to the refractivity of the gas based in parton changing the gas pressure from a non-zero value to a vacuum are notpresent in the first preferred embodiment because of the relative largeequivalent wavelength of (1/l₁)Φ as expressed by Eq. (22).

The resolution of the phase redundancy in ψ₁, if required, presents aproblem similar to the one as subsequently described with respect to therequired resolution of phase redundancy in θ in the fourth embodimentand variants thereof of the present invention. As a consequence, theprocedure described for the resolution of phase redundancy in θ withrespect to the fourth embodiment and variants thereof can be adapted foruse in the resolution of the phase redundancy in ψ₁.

The offset terms involving ζ₁ or/and Q that are present in Eqs. (19) and(20) and defined in Eqs. (2) and (11) are terms that require somecombination of determination and/or monitoring depending on whether χ isvariable in time, whether the refractivity or/and the length L are to bedetermined, respectively, or whether changes in refractivity or/and thelength L are to be determined, respectively. The determination and/ormonitoring of ζ₁ or/and Q as required presents a problem similar to theone as subsequently described with respect to the determination and/ormonitoring of ζ₃ and/or Q in the second and fourth embodiments andvariants thereof of the present invention. As a consequence, theprocedures described for the determination and/or monitoring of ζ₃and/or Q with respect to the second and fourth embodiments and variantsthereof can be adapted for use in the first embodiment for thedetermination and/or monitoring of ζ₁ and/or Q as required.

A first variant of the first preferred embodiment is disclosed whereinthe description of the apparatus of the first variant of the firstembodiment is the same as that given for the apparatus of the firstembodiment except with regard to the detection of beams 217 and 218 ofthe first embodiment shown in FIG. 1a. In the first variant of the firstembodiment, a first portion of beam 217 is detected by a detector (notshown in the figures) creating a signal proportional to s₁, as₁, where ais a constant, and beam 218 and a second portion of beam 217 aredetected by a second single detector (not shown in the figures) creatingsignal S_(b1+2)=bs₁+s₂ where b is a constant. Heterodyne signals as₁ andS_(b1+2) are transmitted as electronic signals 1103 and 1104,respectively, in either digital or analog format, preferably in digitalformat, to electronic processor 109A shown in diagrammatic form in FIG.1c for analysis.

Referring now to FIG. 1c, electronic processor 109A preferably comprisesalphameric numbered elements wherein the numeric component of thealphameric numbers indicate the function of an element, the same numericcomponent/function association as described for the electronicprocessing elements of the first embodiment depicted in FIG. 1b. Thedescription of the steps performed by electronic processor 109A inprocessing heterodyne signals bs₁ and s₂ comprising S_(b1+2) for phasesθ and Φ is the same as corresponding portions, according to the numericcomponent of the alphameric numbers of elements, of the description ofsteps performed by electronic processor 109 in processing heterodynesignals s₁ and s₂ of the first embodiment. The description of the stepsin processing heterodyne signal as₁ by electronic processor 109A forphase ψ₁ is the same as corresponding portions, according to the numericcomponent of the alphameric numbers of elements, of the description ofsteps in the processing of the heterodyne signal s₁ of the firstembodiment by electronic processor 109.

The phases ψ₁, θ, and Φ created by electronic processor 109A formallyhave the same properties as ψ₁, θ, and Φ, respectively, created byelectronic processor 109 of the second embodiment.

The feature of the first variant of the first embodiment which can be asignificant feature is the detection the optical beams creatingheterodyne signals bs₁ and s₂ by a single detector. It will be apparentto those skilled in the art that the single detector feature of thefirst variant of the first embodiment can be important in reducing oreliminating the effects of differences in certain group delays possiblein the first embodiment. The remaining description of the first variantof the first embodiment is the same as corresponding portions of thedescription given for the first embodiment.

A second variant of the first preferred embodiment is disclosed whereinthe description of the apparatus of the second variant of the firstembodiment is the same as that given for the apparatus of the firstembodiment except with regard to the frequencies f₁ and f₂ of drivers 5and 6, respectively, shown in FIG. 1a. In the second variant of thefirst embodiment, the frequencies of the two drivers 5 and 6 are thesame, i.e. f₁=f₂. This feature of the second variant of the firstembodiment eliminates the effects of differences in group delays in thefirst embodiment resulting from f₁≠f₂. The remaining description of thesecond variant of the first embodiment is the same as the correspondingportions of the description given for the first preferred embodiment.

Reference is now made to FIGS. 1a and 1 d which taken together depict indiagrammatic form a third variant of the first preferred embodiment ofthe present invention for measuring and monitoring the refractivity of agas in a measurement path and/or the change in the optical path lengthof the measurement path due to the gas wherein either or both therefractive index of the gas and the physical length of the measurementpath may be changing and where the stability of the adopted lightsources is sufficient and the wavelengths of the light beams generatedby the adopted light sources are harmonically related to a relativeprecision sufficient to meet the required precision imposed on theoutput data by the final end use application. The condition wherein thewavelengths are approximately harmonically related corresponds to thespecial case of the first embodiment in which the ratio (l₁/l₂) isexpressible as the ratio of low order non-zero integers (p₁/p₂), i.e.$\begin{matrix}{{l_{1} = p_{1}},{l_{2} = p_{2}},{( \frac{l_{1}}{l_{2}} ) = ( \frac{p_{1}}{p_{2}} )},p_{1},{p_{2} = 1},2,\ldots \quad,{p_{1} \neq {p_{2}.}}} & (24)\end{matrix}$

The description of the sources of light beams 9 and 10 and of lightbeams 9 and 10 for the second variant of the first embodiment is thesame as that for description of the sources of light beams 9 and 10 andof light beams 9 and 10 given for the first embodiment with theadditional requirement that the wavelengths be harmonically related to arelative precision sufficient to meet the required precision imposed onthe output data by the final end use application. The description of theapparatus for the second variant of the first embodiment depicted inFIG. 1a is the same as corresponding portions of the description givenfor the first embodiment.

Referring now to FIG. 1d, electronic processing means 109B preferablycomprises means 1092A and 1092B for electronically multiplyingtime-dependent arguments α₁(t) and α₂(t), respectively, of heterodynesignals s₁ and s₂, respectively, by coefficients p₁ and p₂,respectively, so as to create two modified heterodyne signals {tildeover (s)}₁ and {tilde over (s)}₂ having the form

{tilde over (s)} _(j) =Ã _(j) cos[p _(j)α_(j)(t)], j=1 and 2.  (25)

The multiplication may be achieved by any one of the conventionalfrequency multiplying techniques commonly known in the art, such assignal squaring followed by electronic filtering.

Referring again to FIG. 1d, electronic processing means 109B preferablycomprises means 1095E for electronically multiplying together, either asan analog or digital process, preferably a digital process, modifiedheterodyne signals {tilde over (s)}₁ and {tilde over (s)}₂ to create asuperheterodyne signal S_({tilde over (1)}×{tilde over (2)}) having themathematical form

S _({tilde over (1)}×{tilde over (2)}) ={tilde over (s)} ₁ {tilde over(s)} ₂.  (26)

The superheterodyne signal S_({tilde over (1)}×{tilde over (2)}) iscomprised of two sidebands with a suppressed carrier and may berewritten as

 S _({tilde over (1)}×{tilde over (2)}) =S_({tilde over (1)}×{tilde over (2)}) ⁺ +S_({tilde over (1)}×{tilde over (2)}) ⁻  (27)

where

S _({tilde over (1)}×{tilde over (2)}) ⁺=½Ã ₁ Ã ₂ cos(2π{tilde over (ν)}t+{tilde over (θ)}),  (28)

S _({tilde over (1)}×{tilde over (2)}) ⁻=½Ã ₁ Ã ₂ cos(2π{tilde over(F)}t+{tilde over (Φ)}),  (29)

{tilde over (ν)}=(p ₁ f ₁ +p ₂ f ₂),  (30)

{tilde over (θ)}=(p ₁ψ₁ +p ₂ 104 ₂),  (31)

{tilde over (F)}=( p ₁ f ₁ −p ₂ f ₂),  (32)

{tilde over (Φ)}=(p ₁ψ₁ −p ₂ 104 ₂).  (3)

Superheterodyne signal S_({tilde over (1)}×{tilde over (2)}) istherefore comprised of two sidebands,S_({tilde over (1)}×{tilde over (2)}) ⁺ andS_({tilde over (1)}×{tilde over (2)}) ⁻, of equal amplitude, onesideband with frequency {tilde over (ν)} and phase {tilde over (θ)} anda second sideband with frequency {tilde over (F)} and phase {tilde over(Φ)}.

Referring once again to FIG. 1d, electronic processor 109B preferablycomprises processor 1093A to separate the two sideband signalsS_({tilde over (1)}×{tilde over (2)}) ⁺ andS_({tilde over (1)}×{tilde over (2)}) ⁻, using filtering or any of thelike techniques for separating two signals that are separated infrequency. The frequency {tilde over (F)} of the lower frequencysideband of the superheterodyne signal can be very much smaller than thefrequency {tilde over (ν)} of the higher frequency sideband of thesuperheterodyne signal as subsequently described in the remainingdiscussion of the third variant of the first embodiment, considerablysimplifying the separating task of processor 1093A. Electronic processor109B further comprises processors 1094F and 1094G to determine thephases {tilde over (θ)} and {tilde over (Φ)} using time-based phasedetection such as a Hilbert transform phase detector (see section 4.1.1of “Phase-locked loops: theory, design, and applications” by R. E. Best,ibid.) or the like and the phases of the drivers 5 and 6.

The phases of the drivers 5 and 6 are transmitted as electrical signalsin either digital or analog format, preferably a digital format, for useas reference signals 101 and 102, respectively, to electronic processor109B. The reference signal for the determination of phases {tilde over(θ)} and {tilde over (Φ)} by way of phase sensitive detection isgenerated by mixing reference signals 101 and 102 and high pass and lowpass filtering, respectively. Electronic processor 109B additionallycomprises processor 1094A to determine the phase shift ψ₁ usingtime-based phase detection or the like, reference signal 101 serving asthe reference signal in phase sensitive detection.

Reference signals, alternatives to reference signals 101 and 102, mayalso be generated by an optical pick off means and detectors (not shownin figures) by splitting off portions of beams 9 and 10 with beamsplitters, preferably non-polarizing beam splitters, mixing the portionof the beam 9 and the portion of beam 10 that are split off, anddetecting the mixed portions to produce heterodyne reference signals.

The quantities p{tilde over (θ)}, p{tilde over (Φ)}, pξ, and pZ of thethird variant of the first embodiment are formally the same as θ, Φ, ξ,and Z, respectively, of the first embodiment with l₁=p₁ and l₂=p₂. Thus,the refractivity (n₁−1) of the gas or changes in L due to the gas in themeasuring path can be expressed in terms of other quantities obtained inthe third variant of the first embodiment by use of the knownrelationships cited in this paragraph and by the use of Eqs. (11), (12),(13), (19), and (20) with l₁=p₁ and l₂=p₂ as specified by Eqs. (24).

A preferred embodiment of the invention having been disclosed in thedescription of the third variant of the first embodiment, the underlyingadvantages of the third variant of the first embodiment will be mademore clear by the following discussion. It is evident from thecalculation of the refractivity by Eq. (7) or the calculation of theeffect of the refractivity of the gas on the optical path by Eq. (14),that the required accuracies to which the superheterodyne sidebandphases {tilde over (θ)} and {tilde over (Φ)} must be determined arerelated to the values of the wavenumbers K and χ. In that the frequency{tilde over (F)} can be very much smaller than the frequency {tilde over(ν)}, and since it is generally easier to calculate the phase with highresolution of an electronic signal of lower frequency, it is generallymost advantageous to rely on a high-accuracy measurement of thesuperheterodyne sideband phase {tilde over (Φ)}. This is readilyachieved in the inventive apparatus when the wavenumbers K and χ arerelated according to Eq. (16), the calculation of the refractivity byEq. (19) or the calculation of the effect of the refractivity of the gason the optical path by Eq. (20) substantially not involving thesuperheterodyne sideband phase {tilde over (θ)}. Further, the magnitudeof the superheterodyne sideband phase {tilde over (Φ)} is less than themagnitude superheterodyne sideband phase {tilde over (θ)}, less by afactor of approximately (n₂−n₁)/(n₂+n₁) as expressed by Eq. (17). Thisgreatly improves in general the phase detection accuracy of the quantity[θ(K/χ)−Φ] that appears in Eqs. (7) and (14) and in particular formoving objects, such as are commonly encountered in microlithographyequipment, which may be coupled to the interferometric apparatus as at267.

Eq. (18) also forms the basis for a conclusion that sources 1 and 2 neednot be phase locked for the third variant of the first embodiment. Eq.(18) is actually a weak condition when viewed in terms of a phase-lockedrequirement for sources 1 and 2. Consider for an example a desiredprecision of ε≅3×10⁻⁶ for measuring the refractivity (n₁−1) of the gasor for the change in the optical path length of the measurement leg dueto the gas, corresponding to a relative distance measuring precision ofapproximately 1×10⁻⁹ in a distance measuring interferometer,(n₁−1)≅3×10⁻⁴, and (n₂−n₁)≅1×10⁻⁵. For the example, the conditionexpressed by Eq. (18) written in terms of source frequencies ν₁ and ν₂instead of wavelengths λ₁ and λ₂, respectively, is $\begin{matrix}{{{v_{2} - {\frac{p_{1}}{p_{2}}v_{1}}}}{3 \times 10^{- 11}{v_{2}.}}} & (34)\end{matrix}$

For source wavelengths in the visible part of the spectrum and for loworder integers for p₁ and p₂, Eq. (34) translates into a condition$\begin{matrix}{{{v_{2} - {\frac{p_{1}}{p_{2}}v_{1}}}}{30\quad {{kHz}.}}} & (35)\end{matrix}$

The result expressed in Eq. (35) is clearly a significantly lessrestrictive condition on the frequencies of sources 1 and 2 than aphase-locked condition.

The remaining description of the third variant of the first embodimentis the same as corresponding portions of the descriptions given for thefirst embodiment.

It will be appreciated by those skilled in the art that alternative dataprocessing may be considered for the third variant of the firstembodiment without departing from the spirit and scope of the presentinvention. For example, it may prove useful to generate the modifiedheterodyne signals by electronically dividing time-dependent argumentsα₁(t) and α₂(t) of heterodyne signals s₁ and s₂, respectively, bycoefficients p₂ and p₁, respectively, so as to create two modifiedheterodyne signals {tilde over (s)}₁′ and {tilde over (s)}₂′ having theforms $\begin{matrix}{{{\overset{\sim}{s}}_{1}^{\prime} = {{\overset{\sim}{A}}_{1}^{\prime}{\cos \lbrack {{\alpha_{1}(t)}/p_{2}} \rbrack}}},{{\overset{\sim}{s}}_{2}^{\prime} = {{\overset{\sim}{A}}_{2}^{\prime}{{\cos \lbrack {{\alpha_{2}(t)}/p_{1}} \rbrack}.}}}} & (36)\end{matrix}$

The dividing may be achieved by any one of the conventional frequencydividing techniques commonly known in the art, such as the use ofphase-locked loops or generation of a rectangle wave signal whichchanges sign at every other zero crossing of the signal whose argumentis being divided by two. The subsequent description of the variant ofthe first embodiment based on modified heterodyne signals {tilde over(s)}₁′ and {tilde over (s)}₂′ is the same as corresponding portions ofthe description of the third variant of the first embodiment based onmodified heterodyne signals {tilde over (s)}₁ and {tilde over (s)}₂.

Another alternative data processing that may be considered for the thirdvariant of the first preferred embodiment without departing from thespirit and scope of the present invention is the addition of themodified heterodyne signals {tilde over (s)}₁ and {tilde over (s)}₂together, rather than multiplying them as in the third variant of thefirst embodiment, resulting in the expression:

S _(A) ={tilde over (s)} ₁ +{tilde over (s)} ₂.  (37)

A superheterodyne signal would be obtained from S_(A) by conventionaltechniques commonly known in the art such as square law detection or bysignal rectification. (cf. Dändliker et al., ibid., and Redman and Wall,ibid.). Further, another alternative signal toS_({tilde over (1)}×{tilde over (2)}) may be generated by selecting theappropriate term in the binomial expansion of (s₁+s₂)^(p+q) through theuse of phase sensitive detection.

Reference is now made to FIGS. 2a-2 f which depict in diagrammatic formthe second preferred embodiment of the present invention for measuringand monitoring the refractivity of a gas in a measurement path and/orthe change in the optical path length of the measurement path due to thegas wherein either or both the refractive index of the gas and thephysical length of the measurement path may be changing and where thestability of the adopted light sources is sufficient and the ratio ofthe wavelengths of the light beams generated by the adopted lightsources is matched to a known ratio value with a relative precisionsufficient to meet the required precision imposed on the output data bythe final end use application.

A preferred method for electronically processing the heterodyne signalss₃ and s₄ is presented herewithin for the case when l₁ and/or l₂ are notlow order integers. For the case when l₁ and l₂ are both low orderintegers and the ratio of the wavelengths matched to the ratio (l₁/l₂)with a relative precision sufficient to meet the required precisionimposed on the output data by the end use application, the preferredprocedure for electronically processing the heterodyne signals s₁ and s₂is the same as the one subsequently set down for the second variant ofthe first preferred embodiment of the present invention.

The second preferred embodiment of the present invention is comprised ofa set of differential plane mirror interferometers, the first embodimentbeing comprised of a polarized Michelson interferometer, wherein thedifferential plane mirror interferometer is well suited to requirementsof micro-lithographic fabrication of integrated circuits. Thedescription of the sources of light beams 9 and 10 and of light beams 9and 10 for the second embodiment is the same as the description of thesources of light beams 9 and 10 and of light beams 9 and 10 given forthe first preferred embodiment of the present invention.

As illustrated in FIG. 2a, beam 9 is incident on differential planemirror interferometer 69 and beam 10 is reflected by mirror 54 as beam12 which is incident on differential plane mirror interferometer 70.Differential plane mirror interferometers 69 and 70, beam splitter 65,and external mirrors furnished by external mirror system 90 compriseinterferometric means for introducing a phase shift ψ₃ between the x andy components of beam 9 and a phase shift ψ₄ between the x and ycomponents of beam 12.

A differential plane mirror interferometer measures the optical pathchanges between two external plane mirrors. In addition, it isinsensitive to thermal and mechanical disturbances that may occur in theinterferometer beam splitting cube and associated optical components.Differential plane mirror interferometer 69 has four exit/return beams17, 25, 117, and 125 as shown in FIG. 2b. Beams 17 and 25 originatingfrom one frequency component of beam 9 comprise one measurement leg andbeams 117 and 125 originating from a second frequency component of beam9 comprise a second measurement leg. Beams for which the first frequencycomponent of beam 9 is the sole progenitor are indicated in FIG. 2b bydashed lines and beams for which the second frequency component of beam9 is the sole progenitor are indicated in FIG. 2b by dotted lines.

Differential plane mirror interferometer 70 has four exit/return beams18, 26, 118, and 126 as shown in FIG. 2c. Beams 18 and 26 originatingfrom one frequency component of beam 12 comprise one measurement leg andbeams 118 and 126 originating from a second frequency component of beam12 comprise a second measurement leg. Beams for which the firstfrequency component of beam 12 is the sole progenitor are indicated inFIG. 2c by dashed lines and beams for which the second frequencycomponent of beam 12 is the sole progenitor are indicated in FIG. 2c bydotted lines.

Beams 17, 25, 117, and 125 are incident on beam splitter 65 and aretransmitted by coating 66, preferably a dichroic coating, as beams E17,E25, E117, and E125, respectively. Beams E17, E25, E117, and E125 areincident on external mirror system 90, illustrated in FIG. 2d, whichresults in beams 27 and 127 shown in FIG. 2b. Beams 127 and 27 containinformation at wavelength λ₁ about the optical path length through thegas in measuring path of external mirror system 90 and about the opticalpath length through a reference path, respectively. Likewise, beams 18,26, 118, and 126 are incident on beam splitter 65 and reflected bydichroic coating 66 as beams E18, E26, E118, and E126, respectively.Beams E18, E26, E118, and E126 are incident on external mirror system90, illustrated in FIG. 2e, which results in beams 28 and 128 shown inFIG. 2c. Beam 128 contains information at wavelength λ₂ about opticalpath lengths through the gas in the measuring path of external mirrorsystem 90 and beam 28 contains information at wavelength λ₂ aboutoptical path lengths through a reference path.

In FIG. 2b, beam 27 is reflected by mirror 63B, a portion of which isreflected by beam splitter 63A, preferably a non-polarizing type, tobecome one component of beam 29. A portion of beam 127 is transmitted bybeam splitter 63A to become a second component of beam 29. Beam 29 is amixed beam, the first and second components of beam 29 having the samelinear polarizations. Beam 29 exits the differential plane mirrorinterferometer 69.

Referring to FIG. 2c, beam 28 is reflected by mirror 58B, a portion ofwhich is reflected by beam splitter 58A, preferably a non-polarizingbeam splitter, to become a first component of beam 30. A portion of beam128 is transmitted by beam splitter 58A to become a second component ofbeam 30. Beam 30 is a mixed beam, the first and second components ofbeam 30 having the same linear polarizations.

The magnitude of phase shifts ψ₃ and ψ₄ are related to the differenceL_(i) between the round-trip physical length of path i of measurementpath 98 and of reference paths shown in FIGS. 2a-2 e according to theformulae $\begin{matrix}{{\phi_{3} = {{\sum\limits_{i = 1}^{i = p}\quad \phi_{3,i}} = {{\sum\limits_{i = 1}^{i = p}\quad {L_{i}k_{1}n_{1i}}} + \zeta_{3}}}},{\phi_{4} = {{\sum\limits_{i = 1}^{i = p}\quad \phi_{4,i}} = {{\sum\limits_{i = 1}^{i = p}\quad {L_{i}k_{2}n_{2i}}} + \zeta_{4}}}},} & (38)\end{matrix}$

where n_(ji) are the refractive indices of gas in path i of measurementpath 98 corresponding to wavenumber k_(j). The nominal value for L_(i)corresponds to twice the spatial separation of mirror surfaces 95 and 96in external mirror system 90 (cf. FIGS. 2d and 2 e). The phase offsetsζ_(j) comprise all contributions to the phase shifts ψ_(j) that are notrelated to the measurement path 98 or reference paths. In FIGS. 2a-2 e,differential plane mirror interferometers 69 and 70, beam splitter 65,and external mirror system 90 are configured so that p=2 so as toillustrate in the simplest manner the function of the apparatus of thesecond preferred embodiment of the present invention.

Eqs. (38) are valid for the case where the paths for one wavelength andthe paths for the second wavelength are substantially coextensive, acase chosen to illustrate in the simplest manner the function of theinvention in the second embodiment. To those skilled in the art, thegeneralization to the case where the respective paths for the twodifferent wavelengths are not substantially coextensive is a straightforward procedure.

Cyclic errors that produce nonlinearities in distance measuringinterferometry (cf. the cited articles by Bobroff) have been omitted inEqs. (38). The description of techniques known to those skilled in theart for either the reduction of the cyclic errors to negligible levelsor for the compensation for the presence of cyclic errors is the same ascorresponding portions of the description given for the first preferredembodiment.

In a next step as shown in FIG. 2a, phase-shifted beams 29 and 30impinge upon photodetectors 185 and 186, respectively, resulting in twoelectrical interference signals, heterodyne signals s₃ and s₄,respectively, preferably by photoelectric detection. The signal s₃corresponds to wavelength λ₁ and signal s₄ corresponds to the wavelengthλ₂. The signals s_(j) have the form the same as that expressed by Eq.(3) with j=3 and 4. Heterodyne signals s₃ and s₄ are transmitted toelectronic processor 209 for analysis as electronic signals 203 and 204,respectively, in either digital or analog format, preferably in digitalformat.

Referring now to FIG. 2f, electronic processor 209 preferably iscomprised of alphameric numbered elements wherein the numeric componentof the alphameric numbers indicate the function of an element, the samenumeric component/function association as described for the electronicprocessing elements of the first embodiment depicted in FIG. 1b. Thedescription of the steps in processing of the heterodyne signals s₃ ands₄ by electronic processor 209 for phases θ and Φ is the same ascorresponding portions, according to the numeric component of thealphameric numbers of elements, of the description of steps in theprocessing of the heterodyne signals s₁ and s₂ of the first embodimentby electronic processor 109.

The phases ψ₃, θ, and Φ created by electronic processor 209 formallyhave the same properties as ψ₁, θ, and Φ, respectively, created byelectronic processor 109 of the first embodiment. Thus, the refractivity(n₁−1) of the gas or changes in L due to the gas in the measuring pathcan be expressed in terms of other quantities obtained in the secondembodiment by use of the known relationships cited in this paragraph andby the use of Eqs. (19) and (20).

The resolution of phase redundancy in ψ₃ is required in the computationof L using Eq. (20) and the resolution of the phase redundancy in ψ₃ isrequired in the computation of changes L using Eq. (20) if χ is variablein time. The resolution of the phase redundancy in ψ₃, if required,presents a problem similar to the one as subsequently described withrespect to the resolution of phase redundancy in θ in the fourthembodiment of the present invention. As a consequence, the proceduresdescribed for the resolution of phase redundancy in θ with respect tothe fourth embodiment can be adapted for use in the resolution of thephase redundancy in θ₃.

The offset terms involving ζ₃ and Q that are present in Eqs. (19) and(20) and defined in Eqs. (2) and (11) are terms that may requiredetermination and monitoring depending on whether the refractivity(n₁−1) and/or L are being measured, whether changes in the refractivity(n₁−1) and/or L are being measured, whether ζ₃ and/or Q are variable intime, and/or whether χ is variable in time. One procedure for thedetermination of θ₃ and Q is based on replacement of mirror 91 of theexternal mirror system 90 with a mirror R91 (not shown in FIGS. 2d and 2e) having a surface R93 corresponding to surface 93 of mirror 91 coatedso as be a reflecting surface for both wavelengths λ₁ and λ₂ andmeasuring the resulting values of ψ₃ and Φ. Let the resulting values ofψ₃ and Φ be ψ_(3R) and Φ_(R), respectively. The quantities ζ₃ and Q arerelated to ψ_(3R) and Φ_(R), respectively, as evident from Eqs. (2) and(19) by the formulae

ζ₃=ψ_(3R),  (39)

Q=−Φ _(R).  (40)

The non-electronic contributions to ζ₃ and Q should be substantiallyconstant in time because of the significant level of compensation thattakes place in the differential plane mirror interferometers 69 and 70,beam splitter 65, and external mirror system 90. The electroniccontributions to ζ₃ and Q may be monitored by purely electronic means(not shown).

It will be apparent to someone skilled in the art that as a consequenceof the incorporation of beam splitter 65 in the second preferredembodiment, polarizing coating 73 of beam splitter 71 and quarter-waveretardation plate 77 need only meet performance specifications at λ₁while polarizing coating 74 of beam splitter 72 and quarter-waveretardation plate 78 need only meet performance specifications at λ₂.This assignment of critical operations according to wavelength asdisclosed in the second embodiment is an important aspect of the presentinvention, particularly in applications requiring precision such as thecase of micro-lithographic fabrication of integrated circuits. However,the assignment of operations according to wavelength need not done asdisclosed in the second preferred embodiment, e.g. the function of beamsplitters 71 and 72 being achieved by a single beam splitter with anappropriately modified polarizing surface, without departing from thespirit or scope of the present invention.

FIG. 2b depicts in schematic form one embodiment of the differentialplane mirror interferometer 69 shown in FIG. 2a. It operates in thefollowing way: beam 9 is incident on beam splitter 55A, preferably apolarizing beam splitter, with a portion of beam 9 being transmitted asbeam 13. A second portion of beam 9 is reflected by beam splitter 55A,subsequently reflected by mirror 55B, and then transmitted by half-wavephase retardation plate 79 as beam 113, the half-wave phase retardationplate 79 rotating by 90° the plane of polarization of the second portionof beam 9 reflected by beam splitter 55A. Beams 13 and 113 have the samepolarizations but still have different frequencies. The function of beamsplitter 55A and mirror 55B is to spatially separate the two frequencycomponents of beam 9 using conventional polarization techniques.

Beams 13 and 113 enter polarizing beam splitter 71, which has apolarizing coating 73, and are transmitted as beams 15 and 115,respectively. Beams 15 and 115 pass through quarter-wave phaseretardation plate 77 and are converted into circularly polarized beams17 and 117, respectively. Beams 17 and 117 are transmitted by beamsplitter 65 with dichroic coating 66, reflected back on themselves bymirrors within external mirror system 90 as illustrated in FIG. 2d, passback through beam splitter 65, and subsequently pass back throughquarter-wave retardation plate 77 and converted into linearly polarizedbeams that are orthogonally polarized to the original incident beams 15and 115. These beams are reflected by polarizing coating 73 to becomebeams 19 and 119, respectively. Beams 19 and 119 are reflected byretroreflector 75 to become beams 21 and 121, respectively. Beams 21 and121 are reflected by polarizing coating 73 to become beams 23 and 123,respectively. Beams 23 and 123 pass through quarter-wave phaseretardation plate 77 and are converted into circularly polarized beams25 and 125, respectively. Beams 25 and 125 are transmitted by beamsplitter 65, reflected back on themselves by mirrors within externalmirror system 90 as illustrated in FIG. 2d, pass back through beamsplitter 65, and subsequently pass back through quarter-wave retardationplate 77 and converted into linearly polarized beams, the linearpolarizations being the same as the linear polarizations of the originalincident beams 15 and 115. These beams are transmitted by polarizingcoating 73 to become beams 27 and 127, respectively.

Beam 27 is reflected by mirror 63B, and then a portion reflected by beamsplitter 63A, preferably a non-polarizing type, as a first component ofbeam 29. Beam 127 is incident on beam splitter 63A with a portion ofbeam 127 being transmitted as a second component of beam 29, the firstand second components of beam 29 having the same linear polarizationsbut still having different frequencies. Phase-shifted beam 29 is a mixedbeam, the first and second components of beam 29 having the same linearpolarizations.

FIG. 2c depicts in schematic form one embodiment of differential planemirror interferometer 70 shown in FIG. 2a. It operates in the followingway: Beam 12 is incident on beam splitter 56A, preferably a polarizingbeam splitter, with a portion of beam 12 being transmitted as beam 14. Asecond portion of beam 12 is reflected by beam splatter 56A,subsequently reflected by mirror 56B, and then transmitted by half-wavephase retardation plate 80 as beam 114, the half-wave phase retardationplate 80 rotating by 90° the plane of polarization of the second portionof beam 12 reflected by beam splitter 56A. Beams 14 and 114 have thesame polarizations but still have different frequencies. The function,in part, of beam splitter 56A and mirror 56B is to spatially separatethe two frequency components of beam 12 using conventional polarizationtechniques.

Beams 14 and 114 enter polarizing beam splitter 72, which has apolarizing coating 74, and are transmitted as beams 16 and 116,respectively. Beams 16 and 116 pass through quarter-wave phaseretardation plate 78 and are converted into circularly polarized beams18 and 118, respectively. Beams 18 and 118 are reflected by beamsplitter 65 with dichroic coating 66, reflected back on themselves bymirrors within external mirror system 90 as illustrated in FIG. 2e,reflected by surface 66 of beam splitter 65 a second time, andsubsequently pass back through quarter-wave retardation plate 78 andconverted into linearly polarized beams that are orthogonally polarizedto the original incident beams 16 and 116. These beams are reflected bypolarizing coating 74 to become beams 20 and 120, respectively. Beams 20and 120 are reflected by retroreflector 76 to become beams 22 and 122,respectively. Beams 22 and 122 are reflected by polarizing coating 74 tobecome beams 24 and 124, respectively. Beams 24 and 124 pass throughquarter-wave phase retardation plate 78 and are converted intocircularly polarized beams 26 and 126, respectively. Beams 26 and 126are reflected by surface 66 of beam splitter 65, reflected back onthemselves by mirrors within external mirror system 90 as illustrated inFIG. 2e, reflected by surface 66 of beam splitter 65 a second time, andsubsequently pass back through quarter-wave retardation plate 78 andconverted into linearly polarized beams, the same linear polarizationsas the linear polarizations of the original incident beams 16 and 116.These beams are transmitted by polarizing coating 74 to become beams 28and 128, respectively. Beams 28 and 128 contain information atwavelength λ₂ about the optical path lengths through the gas inmeasurement path 98 wherein the effects of the refractivity of the gasis to be determined and about the optical path lengths through thereference leg, respectively.

Beam 28 is reflected by mirror 58B, and then a portion reflected by beamsplitter 58A, preferably a non-polarizing type, as a first component ofbeam 30. Beam 128 is incident on beam splitter 58A with a portion ofbeam 128 being transmitted as a second component of beam 30, the firstand second components of beam 30 having the same linear polarizationsbut still having different frequencies. Phase-shifted beam 30 is a mixedbeam, the first and second components of beam 30 having the same linearpolarizations.

The remaining description of the second preferred embodiment is the sameas corresponding portions of the description given for the firstpreferred embodiment.

There are three variants of the second embodiment wherein thedescription of each of the three variants of the second embodiment isthe same as corresponding portions of descriptions given for the threevariants of the first preferred embodiment.

The description of the first preferred embodiment noted that theconfiguration of interferometer illustrated in FIG. 1a is known in theart as a Michelson interferometer. The description of the secondpreferred embodiment noted that the configuration of interferometersillustrated in FIGS. 2a-2 e are known in the art as differential planemirror interferometers. Other forms of the differential plane mirrorinterferometer and forms of other interferometers such as the planemirror interferometer or the angle-compensating interferometer orsimilar device such as is described in an article entitled “Differentialinterferometer arrangements for distance and angle measurements:Principles, advantages and applications” by C. Zanoni, VDI Berichte Nr.749, 93-106 (1989), is preferably incorporated into the apparatus of thefirst embodiment of the present invention as when working with stagescommonly encountered in the micro-lithographic fabrication of integratedcircuits without significantly departing from the spirit and scope ofthe present invention.

The third and fourth preferred embodiments of the present invention andvariants thereof, illustrated in FIGS. 3a-3 b and 4 a-4 c, respectively,are embodiments to measure a refractivity of a gas and/or the change inthe optical path length of a measurement path due to the gas when thecondition set fourth in Eq. (18) for the first and second preferredembodiments and variants thereof is not satisfied, i.e. $\begin{matrix}{{{\frac{\lambda_{1}}{\lambda_{2}} - \frac{l_{1}}{l_{2}}}}{( \frac{l_{2}}{l_{1}} )( {n_{2} - n_{1}} ){ɛ.}}} & (41)\end{matrix}$

Under the condition set fourth in Eq. (41), the approximate ratio,preferably the ratio (K/χ), must be either known or measured inaccordance with Eqs. (7) and (14) for the third and fourth embodimentsand variants thereof in addition to already described quantities inorder to achieve the required accuracy in the determination of arefractivity of the gas and/or the change in the optical path of themeasurement path due to the gas.

Each of the first and second preferred embodiments and variants thereofcan be converted from an apparatus and method for measuring arefractivity of the gas and/or the change in the optical path of themeasurement path due to the gas to an apparatus and method for measuringχ and/or the ratio (K/χ). The conversion, as demonstrated in thefollowing descriptions, is accomplished by changing the measurement legsof the first and second embodiments and variants thereof so that themeasuring paths through a gas in respective measurement paths 298 and 98are replaced by a predetermined medium, preferably a vacuum, and therespective measurement legs have a fixed physical length. Accordingly,the third embodiment and variants thereof are each comprised of anunmodified and a modified apparatus and method from the first embodimentor a variant thereof and the fourth embodiment and variants thereof areeach comprised of an unmodified and a modified apparatus and method fromthe second embodiment of a variant thereof, the modified apparatus andmethod being comprised of the respective unmodified apparatus and methodwith a modified measurement leg.

Reference is now made to FIGS. 3a-3 b that depict in diagrammatic formthe third preferred embodiment of the present invention. The descriptionof the source of light beam 9 of the third embodiment is the same asthat for light beam 9 of the first preferred embodiment and thedescription of the source of light beam 10 of the third embodiment isthe same as that for light beam 10 of the first preferred embodimentexcept that the condition on wavelengths λ₁ and λ₂ expressed by Eq. (18)is replaced by the condition set fourth in Eq. (41). Light beam 9 isreflected by mirror 253A and a first portion reflected by beam splitter253B, preferably a non-polarizing type, to become one component of beam213, the λ₁ component. A second portion of beam 9 reflected by mirror253A is transmitted by beam splitter 253B and reflected by mirror 253 cto become one component of beam 213 b, the λ₁ component. Light beam 10is incident on beam splitter 253B and a first portion transmitted tobecome a second component of beam 213, the λ₂ component. A secondportion of beam 10 is reflected by beam splitter 253B and reflected bymirror 253 c to become a second component of beam 213 b, the λ₂component (see FIG. 3a). The λ₁ and λ₂ components of beams 213 and 213 bare preferably parallel and coextensive, respectively.

Because of the requirement in the third preferred embodiment to measureχ and/or the ratio (K/χ), the third preferred embodiment as described ina preceding paragraph is comprised in part of the same apparatus andmethod as for the first preferred embodiment and of additional means fordetermination of χ and/or the ratio (K/χ). The additional means fordetermination of χ and/or the ratio (K/χ) is the same as the apparatusand method of the first preferred embodiment except for the measurementpath 298. Consequently, a number of elements of the apparatus shown inFIGS. 3a-3 b for determination of χ and/or the ratio (K/χ) performanalogous operations as apparatus for determination of a refractivity ofa gas and/or the change in the optical path length of a measurement pathdue to the gas of the first preferred embodiment, apart from the suffix“b” when referring to apparatus for determination of χ and/or the ratio(K/χ).

The description of interferometer 260 b is the same as that forinterferometer 260 except with respect to the gas in measurement path298 b and the round-trip physical length of the measurement path 298 b.The measurement leg in the interferometer 260 b of the third preferredembodiment includes measurement path 298 b as illustrated in FIGS. 3a,measurement path 298 b preferably being an evacuated volume of fixedlength (L_(b)/2).

The differences in the measurement path 298 b and 298 lead tomodifications of Eqs. (2) such that the magnitude of phase shifts ψ_(1b)and ψ_(2b), counterparts to phase shifts ψ_(i) and ψ₂, respectively, arerelated to the round-trip physical length L_(b) of measurement path 298b and to reference paths as shown in FIG. 3a according to the formulae

ψ_(jb) =L _(b) pk _(j)+ζ_(jb) , j=1 and 2  (42)

In a next step as shown in FIG. 3a, phase-shifted beams 217 b and 218 bimpinge upon photodetectors 85 b and 86 b, respectively, resulting intwo interference signals, heterodyne signals s_(1b) and s_(2b),respectively, preferably by photoelectric detection. The signal s_(1b)corresponds to wavelength λ₁ and signal s_(2b) corresponds to thewavelength λ₂. The signals s_(jb) have the form

 s _(jb) =A _(jb) cos[α_(jb)(t)], j=1 and 2  (43)

where the time-dependent arguments α_(jb)(t) are given by

α_(jb)(t)=2πf _(j) t+ψ _(jb) , j=1 and 2.  (44)

Heterodyne signals s_(1b) and s_(2b) are transmitted to electronicprocessor 109 b for analysis as electronic signals 103 b and 164 b,respectively, in either digital or analog format, preferably in digitalformat.

A preferred method for electronically processing the heterodyne signalss 1b and s 2b is presented herewithin for the case when I₁ and/or I₂ arenot low order integers. For the case when I₁ and I₂ are both low orderintegers and the ratio of the wavelengths matched to the ratio (l₁/l₂)with a relative precision sufficient to meet the required precisionimposed on the output data by the end use application, the preferredprocedure for electronically processing the heterodyne signals s₁ and s₂is the same as the one subsequently set down for the third variant ofthe third preferred embodiment of the present invention.

Referring now to FIG. 3b, electronic processor 109 b further compriseselectronic processors 1094Ab and 1094Bb to determine the phases ψ_(1b)and ψ_(2b), respectively, by either digital or analog signal processes,preferably digital processes, using time-based phase detection such as adigital Hilbert transform phase detector [R. E. Best, ibid.] or the likeand the phase of drivers 5 and 6.

Referring again to FIG. 3b, the phase ψ_(1b) and the phase ψ_(2b) arenext multiplied by l₁/P and l₂/p, respectively, in electronic processors1095Ab and 1095Bb, respectively, preferably by digital processing,resulting in phases (l₁/p)ψ_(1b) and (l₂/p)ψ_(2b), respectively. Thephases (l₁/p)ψ_(1b) and (l₂/p)ψ_(2b) are next added together inelectronic processor 1096Ab and subtracted one from the other inelectronic Processor 1097Ab, preferably by digital processes, to createthe phases θ_(1b) and Φ_(1b), respectively. Formally, $\begin{matrix}{{\vartheta_{1b} = ( {{\frac{l_{1}}{p}\phi_{1b}} + {\frac{l_{2}}{p}\phi_{2b}}} )},} & (45) \\{~{\Phi_{1b} = {( {{\frac{l_{1}}{p}\phi_{1b}} - {\frac{l_{2}}{p}\phi_{2b}}} ).}}} & (46)\end{matrix}$

The phases θ_(1b) and Φ_(1b) are transmitted to computer 110 as signals105 b, in either digital or analog format, preferably in digital format.

The quantities χ and K are related to phase θ_(b) and phase Φ_(b)according to the formulae

χ=(θ_(b)−ξ_(b))/(2L _(b)),  (47)

K=(Φ_(b) −Z _(b))/(2L _(b)),  (48)

where $\begin{matrix}{{\xi_{2b} = ( {{\frac{l_{1}}{p}\zeta_{1b}} + {\frac{l_{2}}{p}\zeta_{2b}}} )},} & (49) \\{Z_{2b} = {( {{\frac{l_{1}}{p}\zeta_{1b}} - {\frac{l_{2}}{p}\zeta_{2b}}} ).}} & (50)\end{matrix}$

Eqs. (47) and (48) show that within a multiplicative factor [1/(2L_(b))]and phase offset terms ξ_(b) and Z_(b), χ and K are equal to the phaseθ_(b) and the phase Φ_(b), respectively.

The ratio (K/χ) can be expressed by the formula $\begin{matrix}{\frac{K}{\chi} = \frac{( {\Phi_{b} - Z_{b}} )}{( {\vartheta_{b} - \xi_{b}} )}} & (51)\end{matrix}$

using Eqs. (47) and (48). Therefore the ratio (K/χ) is obtained bysubstantially dividing Φ_(b) by θ_(b) without the requirement for anaccurate measurement of L to the same precision as required for (K/χ).The phase redundancy of Φ_(b) can be determined as part of the sameprocedure used to remove the phase redundancy of Φ in the unmodifiedapparatus and method of the first preferred embodiment incorporated aspart of the third preferred embodiment.

The determination of the phase offsets ξ_(b) and Z_(b) is a problemsimilar to the one described with respect to the determination of ξ_(b)and Z_(b) in the fourth preferred embodiment. As a consequence, theprocedures described for the determination of ξ_(b) and Z_(b) withrespect to the fourth embodiment can be adapted for determination ofξ_(b) and Z_(b) in the third embodiment.

The refractivity of the gas and/or the change in the optical path lengthof a measurement path due to the gas is subsequently obtained using Eqs.(7) and/or (14), respectively. Because of the non-negligible effect of θin Eqs. (7) and (14), the phase redundancy of θ must also be resolved inaddition to the resolution of the phase redundancy of θ_(b). Theremainder of the description of the third preferred embodiment is thesame as that given for corresponding aspects of the first preferredembodiment except with respect to the description of the procedure forthe resolution of the phase redundancies of θ and of θ_(b). Theresolution of the phase redundancies in θ and θ_(b) is a problem similarto the one as subsequently described with respect to the requiredresolution of phase redundancy in θ and θ_(b) in the fourth embodimentof the present invention. As a consequence, the procedures described forthe resolution of phase redundancies in θ and θ_(b) with respect to thefourth embodiment can be adapted for use in the resolution of the phaseredundancies in θ and θ_(b) for the third embodiment.

There are three variants of the third embodiment wherein the descriptionof each of the three variants of the third embodiment is the same as thedescription given for corresponding portions of the three variants ofthe first preferred embodiment.

Reference is now made to FIGS. 4a-4 c which depict in diagrammatic formthe fourth preferred embodiment of the present invention. Thedescription of the source of light beams 9 and 9 b of the fourthembodiment is the same as that for light beam 9 of the second preferredembodiment and the description of the source of light beams 10 and 10 bof the fourth embodiment is the same as that for light beam 10 of thesecond preferred embodiment except that the condition on wavelengths λ₁and λ₂ expressed by Eq. (18) is replaced by the condition set fourth inEq. (41). Light beams 9 and 9 b of the fourth embodiment are derivedfrom a common light beam by beam splitter 153A, preferably anon-polarizing type, and mirror 153B and light beams 10 and 10 b of thefourth embodiment are derived from a common light beam by beam splitter154A, preferably a non-polarizing type, and mirror 154B (see FIG. 4a).

Because of the requirement in the fourth preferred embodiment to measureχ and/or the ratio (K/χ), the fourth preferred embodiment is comprisedin part of the same apparatus and method as for the second preferredembodiment and of additional means for determination of χ and/or theratio (K/χ). The additional means for determination of χ and/or theratio (K/χ) is the same as the apparatus and method of the secondpreferred embodiment except for the external mirror system 90 b.Consequently, a number of elements of the apparatus shown in FIGS. 4a-4c for determination of χ and/or the ratio (K/χ) perform analogousoperations as apparatus for determination of a refractivity of a gasand/or the change in the optical path length of a measurement path dueto the gas of the second preferred embodiment, apart from the suffix “b”when referring to apparatus for determination of χ and/or the ratio(K/χ).

The external mirror system 90 b of the fourth preferred embodiment isshown in FIGS. 4b and 4 c. The description of external mirror system 90b is the same as that for external mirror system 90 except with respectto the gas in the measurement path 98 and the round-trip physical lengthof the measurement path 98. The measurement leg in the external mirrorsystem 90 b of the fourth preferred embodiment includes measurement path98 b as illustrated in FIGS. 4b and 4 c, measurement path 98 bpreferably being an evacuated volume defined by mirrors 91 b and 92 band a cylinder 99 b of fixed length (L_(b)/2). Referring to FIGS. 4b and4 c, surface 95 b is coated so as to reflect with high efficiency beamsE17 b, E25 b, E18 b, and E26 b and to transmit with high efficiencybeams E117 b, E125 b, E118 b, and E126 b. Surface 96 b is coated toreflect with high efficiency beams E117 b, E125 b, E118 b, and E126 b.

The differences in the external mirror systems 90 b and 90 lead tomodifications of Eqs. (38) such that the magnitude of phase shiftsψ_(3b) and ψ_(4b), counterparts to phase shifts ψ₃ and ψ₄, respectively,are related to the round-trip physical length L_(bi) of path i ofmeasurement path 98 b and to reference paths as shown in FIGS. 4b and 4c according to the formulae $\begin{matrix}{{\phi_{1b} = {{\sum\limits_{i = 1}^{i = p}\quad {L_{bi}k_{1}}} + \zeta_{1b}}},{\phi_{2b} = {{\sum\limits_{i = 1}^{i = p}\quad {L_{bi}k_{2}}} + {\zeta_{2b}.}}}} & (52)\end{matrix}$

For those applications where changes in the measurement path can bemeasured interferometrically, a feature for example of an applicationbased on a distance measuring interferometer employed for measuringchanges in the measurement path (c.f. the second preferred embodiment),the phase redundancy in θ can be resolved by recording the change in θas the movable mirror 92 of the external mirror system 90 is scanned ina controlled manner by translator 67 over a given length from a nullposition, the null position being the position where the physicallengths of the measurement and reference legs are the substantially thesame. The accuracy required for the determination of the null positionis typically less accurate than the accuracy required for otherparameters as exemplified in the following example: for λ₁=0.633 μm,(n₁−1)≅3×10⁻⁴, (n₂−n₁)≅1×10⁻⁵, ε≅10⁻⁹, and the condition set fourth inEq. (17), the desired accuracy for the null position determinationcorresponds to an uncertainty in θ of the order of ±3.

For those applications where the determination of the refractivityand/or or the change in the optical path length due to the gas in ameasurement leg is made and mirror 92 of the external mirror system doesnot have a scanning capability such as considered in the precedingparagraph, other procedures are available for the resolution of thephase redundancies of θ and θ_(b). The effective wavelengths of θ andθ_(b) are substantially the same so that only procedures for theresolution of phase redundancy in either θ or θ_(b) need be described.

The second procedure described for the resolution of the phaseredundancy of Φ in the description of the second embodiment can beadapted for the resolution of the phase redundancies of θ_(b), thesecond procedure being based on the use of a series of external mirrorsystems of type 90 b where the series of round-trip physical lengths ofthe series of external mirror systems form a geometric progression. Thesmallest or first round-trip physical length in the series of round-tripphysical lengths will be approximately λ₁/8 divided by the relativeprecision that the initial value of θ_(b) is known. The secondround-trip physical length in the series of round-trip physical lengthswill be approximately the length of the first round-trip physical lengthin the series of round-trip physical lengths divided by the relativeprecision that θ_(b) is measured using the first round-trip physicallength in the series of round-trip physical lengths. This is again ageometric progression procedure, the resulting series of round-tripphysical lengths forming a geometric progression, which is continueduntil the physical length of the external mirror system 90 b used tomeasure the refractivity or the change in optical path length due to therefractivity of the gas would be exceeded if the number in the series ofround-trip physical lengths were incremented by one. For the resolutionof phase redundancy in θ_(b), a typical round-trip physical length forthe first round-trip physical length in the series of round-tripphysical lengths is of the order of 0.5 mm, a typical round-tripphysical length for the second round-trip physical length in the seriesof round-trip physical lengths is of the order of 50 mm, and a typicalround-trip physical length for a third round-trip physical length in theseries of round-trip physical lengths if required is of the order of5000 mm. The physical lengths in the series of physical lengths used forthe resolution of phase redundancy in Φ_(b) are typically orders ofmagnitude larger than the physical lengths in the series of physicallengths used for the resolution of phase redundancy in θ_(b).

A third procedure is based upon the use of a source (not shown in FIGS.4a-4 c) of a series of known wavelengths and measuring θ_(b) for thesewavelengths. The number of known wavelengths required for the resolutionof the phase redundancy is generally comprised of a small set.

Another procedure to resolve the phase redundancy in θ_(b) is to observethe changes in θ_(b) as the measuring path 98 b is changed from gas toan evacuated state (the vacuum pump and requisite gas handling systemare not shown in FIGS. 4a-4 c). The problems normally encountered inmeasuring absolute values for refractivity and changes in the opticalpath length due to the refractivity of the gas based in part on changingthe gas pressure from a non-zero value to a vacuum are not present inthe third preferred embodiment because of a relatively large uncertaintyof the order of ±3 typically permitted in the determination of θ_(b).

The offset terms ξ_(b) and Z_(b) that are present in Eq. (51) anddefined in Eqs. (47) and (48), respectively, are terms that may requiredetermination and may require monitoring if variable in time. Oneprocedure for the determination of ξ_(b) and Z_(b) is based onreplacement of mirror 91 b of the external mirror system 90 b with amirror Z91 b (not shown in FIGS. 4a-4 c) having a surface Z93 bcorresponding to surface 93 b of mirror 91 b coated so as be areflecting surface for both wavelengths λ₁ and λ₂ and measuring theresulting θ_(b) and Φ_(b). Let the resulting values of θ_(b) and Φ_(b)be θ_(bR) and Φ_(bR), respectively. The quantities ξ_(b) and Z_(b) arerelated to θ_(bR) and Φ_(bR), respectively, as evident from Eqs. (47)and (48) by the formulae

 ξ_(b)=θ_(bR),  (53)

Z _(b)=Φ_(bR).  (54)

The non-electronic contributions to ξ_(b) and Z_(b) should besubstantially constant in time because of the significant level ofcompensation that takes place in the differential plane mirrorinterferometers 69 b and 70 b, beam splitter 65 b, and external mirrorsystem 90 b. The electronic contributions to ξ_(b) and Z_(b) aremonitored by purely electronic means (not shown).

The wavenumber χ is calculated by the computer using Eq. (47) and themeasured values for θ_(b) and ξ_(b). The ratio K/χ is calculated by thecomputer using Eq. (51)

The refractivity of a gas and/or the change in the optical path lengthof a measurement path due to the gas is subsequently obtained using Eqs.(7) and/or (14), respectively. The remainder of the description of thefourth preferred embodiment is the same as that given for correspondingportions of the second and third preferred embodiments.

There are three variants of the fourth embodiment wherein thedescription of each of the three variants of the fourth embodiment isthe same as the description given for corresponding portions of thethree variants of the second preferred embodiment.

It will be appreciated by those skilled in the art that the wavelengthλ₁ of the light beam used for the determination of ψ₁ in Eqs. (14) and(20) may be different from both of the two wavelengths used to determinethe change in the optical path length of the measuring path due to gasin the measuring path without departing from the scope and spirit of thepresent invention. The requisite reciprocal dispersive power Γ₃ would bedefined in terms of the indices of refraction n₁, n₂, and n₃ of the gasat the three wavelengths λ₁, λ₂, and λ₃, respectively, according to theformula $\begin{matrix}{\Gamma_{3} = \frac{( {n_{1} - 1} )}{( {n_{3} - n_{2}} )}} & (55)\end{matrix}$

for λ₃<λ₂.

It will be further appreciated by those skilled in the art that the twofrequency components of either or both beams 9 and 10 may be spatiallyseparated at any point following the means for introducing the frequencyshifts and prior to entering the respective interferometers of thedescribed preferred embodiments without departing from the scope andspirit of the present invention. If the two frequency components of theeither of the two beams are spatially separated for any significantdistance from the respective interferometer, it may be necessary toemploy alternative reference beams such as described in the firstembodiment.

It will also be appreciated by those skilled in the art that thedifferential plane mirror interferometer and the external mirror systemof the additional means for the determination of χ and/or the ratio(K/χ) in the fourth preferred embodiment may be configured such that oneof the light beams corresponding to one of the wavelengths may enter andexit from one end of the external mirror system and a second of thelight beams corresponding to a differing second wavelength may enter andexit from an opposite end of the external mirror system in contrast tothe same end as disclosed in the fourth preferred embodiment withoutdeparting from the scope or spirit of the invention as defined in theclaims. With the reconfiguring of the external mirror system, beamsplitter 65 b may obviously be omitted, the light beams of differingwavelengths entering and exiting through the mirrors 91 b and 92 b withthe reflecting and transmitting coatings on mirror surfaces 95 b and 96b having been reconfigured accordingly.

The illustrations in FIGS. 2a-2 e and 4 a-4 c depict two preferredembodiments of the present invention wherein all of the optical beamsfor an embodiment are in a single plane. Clearly, modifications usingmultiple planes can be made to one or more of the two preferredembodiments and variants thereof without departing from the scope andspirit of the invention.

The second and fourth preferred embodiments of the present inventionhave external mirror systems 90 b and/or 90 wherein the measurementpaths for λ₁ and λ₂ have the same round-trip physical lengths and thereference paths for λ₁ and λ₂ have the same round-trip physical lengths.It will be appreciated by those skilled in the art that the measurementpaths for λ₁ and λ₂ can have different physical lengths and thereference paths for λ₁ and λ₂ can have different physical lengthswithout departing from the scope and spirit of the present invention asdefined in the claims. It will be further appreciated by those skilledin the art that the measurement paths for λ₁ and λ₂ can be physicallydisplaced one from the other and the reference paths for λ₁ and λ₂ canbe physically displaced one from the other without departing from thescope and spirit of the present invention as defined in the claimsalthough there may be some degradation in performance with regardfrequency response of the embodiments and/or in accuracy of calculatedquantities due to for example spatial gradients in the refractivity of agas in a measurement path.

It will be appreciated by those skilled in the art that alternative dataprocessing may be considered for the four preferred embodiments andvariants thereof of the present invention without departing from thespirit and scope of the present invention.

The four preferred embodiments and variants thereof of the presentinvention are all configured for use of heterodyne detection. It will beappreciated by those skilled in the art that homodyne detection can beemployed in each of the four preferred embodiments and variants thereofwithout departing from the scope and spirit of the present invention asdefined in the claims. Homodyne receivers would be employed such asdisclosed in commonly owned U.S. Pat. No. 5,663,793 entitled “HomodyneInterferometric Receiver and Method,” issued Sep. 2, 1997 in the name ofP. de Groot. The computation of the refractivity of a gas and/or thechange in the optical path length of a measurement path due to the gaswould be obtained for example in the homodyne version of the firstpreferred embodiment directly from homodyne phases ψ_(1H) and ψ_(2H),the homodyne phases ψ_(1H) and ψ_(2H) being counterparts to phases ψ₁and ψ₂ of the first preferred embodiment, and with homodyne versions ofEqs. (7) and (14).

The third and fourth preferred embodiments of the present inventionmeasure the ratio (K/χ) and/or χ and use the measured values of (K/χ)and/or χ in the computation of the refractivity of a gas and/or thechange in the optical path length of a measurement path due to the gas.It will be appreciated by those skilled in the art that the measuredvalues of (K/χ) and/or χ can be used as error signals in a feedbacksystem such the condition expressed by Eq. (18) is satisfied and/or suchthat χ is constant without departing from the scope and spirit of thepresent invention as defined in the claims. The measured value of (K/χ)and/or χ in the feedback system are sent to either source 1 and/orsource 2 and used to control the respective wavelengths of either source1 and/or source 2, for example by controlling the injection currentand/or temperature of a diode laser or the cavity frequency of anexternal cavity diode laser.

It will be appreciated by those skilled in the art that combinations ofthe means of the third and fourth preferred embodiments to measure theratio (K/χ) and/or χ and of the means of the first and second preferredembodiments may be used to determine the refractivity of a gas and/orthe change in the optical path length of a measurement path due to thegas other than the combinations used in the third and fourth preferredembodiments without departing from the scope or spirit of the inventionas defined in the claims.

Reference is now made to FIG. 5 which is a generalized flowchartdepicting via blocks 500-526 various steps for practicing an inventivemethod for measuring and monitoring the refractivity of a gas in ameasurement path and/or the change in the optical path length of themeasurement path due to the gas wherein the refractivity of the gas maybe changing and/or the physical length of the measurement path may bechanging. While it will be evident that the inventive method depicted inFIG. 5 may be carried out using the inventive apparatus disclosedhereinabove, it will also be apparent to those skilled in the art thatit may also be implemented with apparatus other than that disclosed. Forexample, it will be apparent that one need not use differential planemirror interferometers such as that used in the preferred embodiments,but rather may use other conventional interferometric arrangements solong as the required reference and measurement legs are present. Inaddition, it will be evident that one may use either a homodyne approachor one in which heterodyning techniques are advantageously employed. Aswill be further appreciated, many of the steps in FIG. 5 may be carriedout via appropriate software run on a general purpose computer or asuitably programmed microprocessor either of which may be used tocontrol other elements of the system as needed.

As seen in FIG. 5, one starts in block 500 by providing two or morelight beams having different wavelengths which preferably have anapproximate approximate relationship as previously described. In block502, the light beams are separated into components which in block 504are preferably altered by either polarization or spatial encoding, orfrequency shifting or both. Otherwise, the light beams may simply beleft unaltered and passed through to block 506.

As shown in blocks 522 and 524, the relationship of the wavelengths ofthe light beams may be monitored and if their wavelengths are not withinthe limits previously discussed, one can adopt corrective measures tocompensate from departures of the relationship of the wavelengths fromthe desired relationship of the wavelengths. Either the departures canbe used to provide feedback to control the wavelengths of the light beamsources or corrections can be established and used in subsequentcalculations which are influenced by departures or some combination ofboth approaches can be implemented.

In parallel or contemporaneously with generating the light beams inblock 500, one also provides as indicated in block 526 an interferometerhaving two legs, a reference leg and the other a measurement leg whereina portion of the measurement path is in a gas whose refractivity and/oreffect on the optical path length of the measurement path are to bemeasured.

As shown by blocks 506 and 508, the previously generated light beamcomponents are introduced into the interferometer legs so that eachcomponent has its phase shifted based on the optical path length itexperiences in traveling through the physical length of its assignedleg.

After the beams emerge from block 508, they are combined in block 510 togenerate a mixed optical signal. These mixed optical signals are thensent to block 512 where by means of photodetection correspondingelectrical signals, preferably heterodyne, are generated, and theseelectrical signals contain information about the relative phases betweenthe light beam components. Preferably the electrical signals areheterodyne signals brought about by previously frequency shiftingtreatment.

In block 514, the electrical signals may be directly analyzed to extractrelative phase information which can then be passed on to blocks 516-520or, superheterodyne signals are generated, or modified heterodyne andthen superheterodyne signals, or modified heterodyne signals, which arethen subsequently analyzed for the relative phase information.

In block 516, any phase ambiguities in homodyne, heterodyne, and/orsuperheterodyne signals are resolved, preferably by means andcalculations previously elaborated in connection with describing thepreferred embodiments.

In block 518, the refractivity of the gas and/or the effect of therefractivity of the gas on the optical path length of the measurementpath are calculated, corrections are applied as previously described,and output signals are generated for subsequent downstream applicationsor data format requirements.

Those skilled in the art may make other changes to the inventiveapparatus and methods without departing from the scope of the inventiveteachings. Therefore, it is intended that the embodiments shown anddescribed be considered as illustrative and not in a limiting sense.

The interferometry systems described above can be especially useful inlithography applications (as, for example, represented at 267) used forfabricating large scale integrated circuits such as computer chips andthe like. Lithography is the key technology driver for the semiconductormanufacturing industry. Overlay improvement is one of the five mostdifficult challenges down to and below 100 nm line widths (designrules), see for example the Semiconductor Industry Roadmap, p82 (1997).Overlay depends directly on the performance, i.e. accuracy andprecision, of the distance measuring interferometers used to positionthe wafer and reticle (or mask) stages. Since a lithography tool mayproduce $50-100M/year of product, the economic value from improvedperformance distance measuring interferometers is substantial. Each 1%increase in yield of the lithography tool results in approximately$1M/year economic benefit to the integrated circuit manufacturer andsubstantial competitive advantage to the lithography tool vendor.

The function of a lithography tool is to direct spatially patternedradiation onto a photoresist-coated wafer. The process involvesdetermining which location of the wafer is to receive the radiation(alignment) and applying the radiation to the photoresist at thatlocation (exposure).

To properly position the wafer, the wafer includes alignment marks onthe wafer that can be measured by dedicated sensors. The measuredpositions of the alignment marks define the location of the wafer withinthe tool. This information, along with a specification of the desiredpatterning of the wafer surface, guides the alignment of the waferrelative to the spatially patterned radiation. Based on suchinformation, a translatable stage supporting the photoresist-coatedwafer moves the wafer such that the radiation will expose the correctlocation of the wafer.

During exposure, a radiation source illuminates a patterned reticle,which scatters the radiation to produce the spatially patternedradiation. The reticle is also referred to as a mask, and these termsare used interchangeably below. In the case of reduction lithography, areduction lens collects the scattered radiation and forms a reducedimage of the reticle pattern. Alternatively, in the case of proximityprinting, the scattered radiation propagates a small distance (typicallyon the order of microns) before contacting the wafer to produce a 1:1image of the reticle pattern. The radiation initiates photo-chemicalprocesses in the photoresist that convert the radiation pattern into alatent image within the photoresist.

The interferometry systems described above are important components ofthe positioning mechanisms that control the position of the wafer andreticle, and register the reticle image on the wafer.

In general, the lithography system, also referred to as an exposuresystem, typically includes an illumination system and a waferpositioning system. The illumination system includes a radiation sourcefor providing radiation such as ultraviolet, visible, x-ray, electron,or ion radiation, and a reticle or mask for imparting the pattern to theradiation, thereby generating the spatially patterned radiation. Inaddition, for the case of reduction lithography, the illumination systemcan include a lens assembly for imaging the spatially patternedradiation onto the wafer. The imaged radiation exposes photoresistcoated onto the wafer. The illumination system also includes a maskstage for supporting the mask and a positioning system for adjusting theposition of the mask stage relative to the radiation directed throughthe mask. The wafer positioning system includes a wafer stage forsupporting the wafer and a positioning system for adjusting the positionof the wafer stage relative to the imaged radiation. Fabrication ofintegrated circuits can include multiple exposing steps. For a generalreference on lithography, see, for example, J. R. Sheats and B. W.Smith, in Microlithography: Science and Technology (Marcel Dekker, Inc.,New York, 1998), the contents of which are incorporated herein byreference.

The interferometry systems described above can be used to preciselymeasure the positions of each of the wafer stage and mask stage relativeto other components of the exposure system, such as the lens assembly,radiation source, or support structure. In such cases, theinterferometry system can be attached to a stationary structure and themeasurement object attached to a movable element such as one of the maskand wafer stages. Alternatively, the situation can be reversed, with theinterferometry system attached to a movable object and the measurementobject attached to a stationary object.

More generally, the interferometry systems can be used to measure theposition of any one component of the exposure system relative to anyother component of the exposure system in which the interferometrysystem is attached, or supported by one of the components and themeasurement object is attached, or is supported by the other of thecomponents.

An example of a lithography scanner 600 using an interferometry system626 is shown in FIG. 6a. The interferometry system is used to preciselymeasure the position of a wafer within an exposure system. Here, stage622 is used to position the wafer relative to an exposure station.Scanner 600 comprises a frame 602, which carries other supportstructures and various components carried on those structures. Anexposure base 604 has mounted on top of it a lens housing 606 atop ofwhich is mounted a reticle or mask stage 616 used to support a reticleor mask. A positioning system for positioning the mask relative to theexposure station is indicated schematically by element 617. Positioningsystem 617 can include, e.g., piezoelectric transducer elements andcorresponding control electronics. Although, it is not included in thisdescribed embodiment, one or more of the interferometry systemsdescribed above can also be used to precisely measure the position ofthe mask stage as well as other moveable elements whose position must beaccurately monitored in processes for fabricating lithographicstructures (see supra Sheats and Smith Microlithography: Science andTechnology).

Suspended below exposure base 604 is a support base 613 that carrieswafer stage 622. Stage 622 includes a plane mirror for reflecting ameasurement beam 654 directed to the stage by interferometry system 626.A positioning system for positioning stage 622 relative tointerferometry system 626 is indicated schematically by element 619.Positioning system 619 can include, e.g., piezoelectric transducerelements and corresponding control electronics. The measurement beamreflects back to the interferometry system, which is mounted on exposurebase 604. The interferometry system can be any of the embodimentsdescribed previously.

During operation, a radiation beam 610, e.g., an ultraviolet (UV) beamfrom a UV laser (not shown), passes through a beam shaping opticsassembly 612 and travels downward after reflecting from mirror 614.Thereafter, the radiation beam passes through a mask (not shown) carriedby mask stage 616. The mask (not shown) is imaged onto a wafer (notshown) on wafer stage 622 via a lens assembly 608 carried in a lenshousing 606. Base 604 and the various components supported by it areisolated from environmental vibrations by a damping system depicted byspring 620.

In other embodiments of the lithographic scanner, one or more of theinterferometry systems described previously can be used to measuredistance along multiple axes and angles associated for example with, butnot limited to, the wafer and reticle (or mask) stages. Also, ratherthan a UV laser beam, other beams can be used to expose the waferincluding, e.g., x-ray beams, electron beams, ion beams, and visibleoptical beams.

In addition, the lithographic scanner can include a column reference inwhich interferometry system 626 directs the reference beam to lenshousing 606 or some other structure that directs the radiation beamrather than a reference path internal to the interferometry system. Theinterference signal produce by interferometry system 626 when combiningmeasurement beam 654 reflected from stage 622 and the reference beamreflected from lens housing 606 indicates changes in the position of thestage relative to the radiation beam. Furthermore, in other embodimentsthe interferometry system 626 can be positioned to measure changes inthe position of reticle (or mask) stage 616 or other movable componentsof the scanner system. Finally, the interferometry systems can be usedin a similar fashion with lithography systems involving steppers, inaddition to, or rather than, scanners.

As is well known in the art, lithography is a critical part ofmanufacturing methods for making semiconducting devices. For example,U.S. Pat. No. 5,483,343 outlines steps for such manufacturing methods.These steps are described below with reference to FIGS. 6b and 6 c. FIG.6b is a flow chart of the sequence of manufacturing a semiconductordevice such as a semiconductor chip (e.g. IC or LSI), a liquid crystalpanel or a CCD. Step 651 is a design process for designing the circuitof a semiconductor device. Step 652 is a process for manufacturing amask on the basis of the circuit pattern design. Step 653 is a processfor manufacturing a wafer by using a material such as silicon.

Step 654 is a wafer process which is called a pre-process wherein, byusing the so prepared mask and wafer, circuits are formed on the waferthrough lithography. Step 655 is an assembling step, which is called apost-process wherein the wafer processed by step 654 is formed intosemiconductor chips. This step includes assembling (dicing and bonding)and packaging (chip sealing). Step 656 is an inspection step whereinoperability check, durability check, and so on of the semiconductordevices produced by step 655 are carried out. With these processes,semiconductor devices are finished and they are shipped (step 657).

FIG. 6c is a flow chart showing details of the wafer process. Step 661is an oxidation process for oxidizing the surface of a wafer. Step 662is a CVD process for forming an insulating film on the wafer surface.Step 663 is an electrode forming process for forming electrodes on thewafer by vapor deposition. Step 664 is an ion implanting process forimplanting ions to the wafer. Step 665 is a photoresist process forapplying a photoresist (photosensitive material) to the wafer. Step 666is an exposure process for printing, by exposure, the circuit pattern ofthe mask on the wafer through the exposure apparatus described above.Step 667 is a developing process for developing the exposed wafer. Step668 is an etching process for removing portions other than the developedphotoresist image. Step 669 is a photoresist separation process forseparating the photoresist material remaining on the wafer after beingsubjected to the etching process. By repeating these processes, circuitpatterns are formed and superimposed on the wafer.

The interferometry systems described above can also be used in otherapplications in which the relative position of an object needs to bemeasured precisely. For example, in applications in which a write beamsuch as a laser, x-ray, ion, or electron beam, marks a pattern onto asubstrate as either the substrate or beam moves, the interferometrysystems can be used to measure the relative movement between thesubstrate and write beam.

As an example, a schematic of a beam writing system 700 is shown in FIG.7. A source 710 generates a write beam 712, and a beam focusing assembly714 directs the radiation beam to a substrate 716 supported by a movablestage 718. To determine the relative position of the stage, aninterferometry system 720 directs a reference beam 722 to a mirror 724mounted on beam focusing assembly 714 and a measurement beam 726 to amirror 728 mounted on stage 718. Interferometry system 720 can be any ofthe interferometry systems described previously. Changes in the positionmeasured by the interferometry system correspond to changes in therelative position of write beam 712 on substrate 716. Interferometrysystem 720 sends a measurement signal 732 to controller 730 that isindicative of the relative position of write beam 712 on substrate 716.Controller 730 sends an output signal 734 to a base 736 that supportsand positions stage 718. In addition, controller 730 sends a signal 738to source 710 to vary the intensity of, or block, write beam 712 so thatthe write beam contacts the substrate with an intensity sufficient tocause photophysical or photochemical change only at selected positionsof the substrate. Furthermore, in some embodiments, controller 730 cancause beam focusing assembly 714 to scan the write beam over a region ofthe substrate, e.g., using signal 744. As a result, controller 730directs the other components of the system to pattern the substrate. Thepatterning is typically based on an electronic design pattern stored inthe controller. In some applications the write beam patterns aphotoresist coated on the susbstrate and in other applications the writebeam directly patterns, e.g., etches, the substrate.

An important application of such a system is the fabrication of masksand reticles used in the lithography methods described previously. Forexample, to fabricate a lithography mask an electron beam can be used topattern a chromium-coated glass substrate. In such cases where the writebeam is an electron beam, the beam writing system encloses the electronbeam path in a vacuum. Also, in cases where the write beam is, e.g., anelectron or ion beam, the beam focusing assembly includes electric fieldgenerators such as quadrapole lenses for focusing and directing thecharged particles onto the substrate under vacuum. In other cases wherethe write beam is a radiation beam, e.g., x-ray, UV, or visibleradiation, the beam focusing assembly includes corresponding optics forfocusing and directing the radiation to the substrate.

Yet other changes may be made to the invention. For example, it may bedesirable in certain applications to monitor the refractive index of thegas contained on both the reference and in the measurement legs of theinterferometer. Examples include the well-known column reference styleof interferometer, in which the reference leg comprises a target opticplaced at one position within a mechanical system, and the measurementleg comprises a target optic placed at a different position within thesame mechanical system. Another example application relates to themeasurement of small angles, for which both the measurement andreference beams impinge upon the same target optic but at a smallphysical offset, thereby providing a sensitive measure of the angularorientation of the target optic. These applications and configurationsare well known to those skilled in the art and the necessarymodifications are intended to be within the scope of the invention.

Additional alternative means of achieving substantial insensitivity toDoppler shifting in a heterodyne interferometer is to track the Dopplershift and compensate by either (1) adjusting the frequency differencebetween the reference and measurement beams, (2) adjusting the clockfrequency of one or both of the electronic A/D modules or (3) anysimilar means of continuously matching the apparent heterodyne beatfrequency of the two wavelengths by active adjustment of the drive ordetection electronics.

It is understood that while the invention has been described inconjunction with the detailed description thereof, the foregoingdescription is intended to illustrate and not limit the scope of theinvention, which is defined by the scope of the appended claims.

What is claimed is:
 1. Interferometric apparatus for measuring theeffects of the refractive index of a gas in a measurement path, saidinterferometric apparatus comprising: interferometer means comprisingfirst and second measurement legs, said first and second measurementlegs having optical paths structured and arranged such that at least oneof them has a variable physical length and at least one of them is atleast in part occupied by the gas, the optical path length differencebetween said first and second measurement legs varying in accordancewith the difference between the respective physical lengths of theiroptical paths and the properties of said gas; means for generating atleast two light beams having different wavelengths; means forintroducing first and second predetermined portions of each of saidlight beams into said first and second measurement legs, respectively,of said interferometer means so that each of at least one of said firstand second predetermined portions of said light beams travels throughsaid first and second measurement legs along predetermined optical pathswith the same number of passes, said predetermined first and secondportions of said light beams emerging from said interferometer means asexit beams containing information about the respective optical pathlengths through said first and second measurement legs at saidwavelengths; means for combining said exit beams to produce mixedoptical signals containing information corresponding to the phasedifferences between each of said exit beams from corresponding ones ofsaid predetermined optical paths of said first and second measurementlegs at said wavelengths; means for detecting said mixed optical signalsand generating electrical interference signals containing informationcorresponding to the effects of the index of refraction of the gas atsaid different beam wavelengths and the difference in physical pathlengths of said measurement legs and their relative rate of change; andelectronic means for analyzing said electrical interference signals todetermine the effects of said gas in said measurement leg(s) whilecompensating for the relative rates at which the physical path lengthsof said first and second measurement legs are changing, wherein saidinformation corresponding to said phase differences in said mixedoptical signals are phase shifts ψ_(j) related to the differences intotal round-trip physical lengths pL of said measurement legs occupiedby said gas according to the formulae  ψ_(j) =Lpk _(j) n _(j)+ξ_(j) ,j=1,2, . . . where k_(j)=2π/ζ_(j), p is the number of multiple passesthrough the at least one of said first and second measurement legs, andn_(j) are the refractive indices of gas in said at least one of saidmeasurement legs occupied by the gas corresponding to wavelength, λ_(j),and ζ_(j) are phase offsets not associated with optical paths andwherein said electronic means is further configured and arranged tocreate phases θ and Φ where${\vartheta = ( {{\frac{l_{1}}{p}\phi_{1}} + {\frac{l_{2}}{p}\phi_{2}}} )},{{{and}\quad \Phi} = ( {{\frac{l_{1}}{p}\phi_{1}} - {\frac{l_{2}}{p}\phi_{2}}} )}$

where l₁ and l₂ are non-integer values.
 2. The interferometric apparatusof claim 1 wherein the refractivity of the gas, (n₁−1) is calculatedusing the formula:${{n_{1} - 1} = {\frac{\Gamma}{\chi \quad {L\lbrack {1 - ( {K/\chi} )^{2}} \rbrack}}\{ {\lbrack {{\vartheta ( {K/\chi} )} - \Phi} \rbrack - Q} \}}},$

where χ=(l₁K₁+l₂k₂)/2, K=(l₁k₁−l₂k₂)/2 and${\Gamma = \frac{n_{1} - 1}{n_{2} - n_{1}}},$

the quantity Γ being the reciprocal dispersive power of the gas which issubstantially independent of environmental conditions and turbulence inthe gas and the offset terms Q and ζ_(i) are defined as Q=ξ(K/χ)−Z where${\xi = ( {{\frac{l_{1}}{p}\zeta_{1}} + {\frac{l_{2}}{p}\zeta_{2}}} )},{Z = ( {{\frac{l_{1}}{p}\zeta_{1}} - {\frac{l_{2}}{p}\zeta_{2}}} )}$

with ξ and Z being determinable quantities.
 3. The interferometricapparatus of claim 2 wherein electronic means is further configured andarranged to calculate a physical distance, L, independent of the effectsof the refractive index of the gas in the measurement path using theformula$L = {\frac{1}{( {\chi + K} )}\{ {{\frac{l_{1}}{p}( {\phi_{1} - \zeta_{1}} )} - {\frac{\Gamma}{\lbrack {1 - ( {K/\chi} )} \rbrack}\lbrack {{( {K/\chi} )\vartheta} - \Phi - Q} \rbrack}} \}}$

where the ratio of the wavelengths can be expressed in terms of (K/χ)with$\frac{\lambda_{1}}{\lambda_{2}} = {{( \frac{l_{1}}{l_{2}} )\lbrack \frac{1 - ( {K/\chi} )}{1 + ( {K/\chi} )} \rbrack}.}$


4. The interferometric apparatus of claim 1 wherein said electronicmeans is further configured and arranged to compensate for differencesin group delay experienced by said electrical interference signals. 5.Interferometric method for measuring the effects of the refractive indexof a gas in a measurement path, said interferometric apparatuscomprising: providing an interferometer means comprising a first andsecond measurement legs, said first and second measurement legs havingoptical paths structured and arranged such that at least one of them hasa variable physical length and at least one of them is at least in partoccupied by gas, the optical path length difference between said firstand second measurement legs varying in accordance with the difference inthe respective physical lengths of their optical paths and theproperties of said gas; generating at least two light beams havingdifferent wavelengths; introducing first and second predeterminedportions of each of said light beams into said first and secondmeasurement legs, respectively, of said interferometer means so thateach of at least one of said first and second predetermined portions ofsaid light beams travels through said first and second measurement legsalong predetermined optical paths with the same number of passes, saidpredetermined first and second portions of said light beams emergingfrom said interferometer means as exit beams containing informationabout the respective optical path lengths through said first and secondmeasurement legs at said wavelengths; combining said exit beams toproduce mixed optical signals containing information corresponding tothe phase differences between each of said exit beams from correspondingones of said predetermined optical paths of said first and secondmeasurement legs at said wavelengths; detecting said mixed optical signsand generating electrical interference signals containing informationcorresponding to the effects of the index of refraction of the gas atsaid different beam wavelengths and the relative physical path lengthsbetween said first and second measurement legs and their relative ratesof change; and electronically analyzing said interference electricalsignals to determine the effects of said gas in said measurement leg(s)while compensating for the relative rates at which the physical pathlengths of said first and second measurement legs are changing, whereinsaid information corresponding to said phase differences in said mixedoptical signals are phase shifts ψ_(j) related to the differences intotal round-trip physical lengths pL of said measurement legs occupiedby said gas according to the formulae  ψ_(j) =Lpk _(j) n _(j)+ζ_(j) ,j=1,2, . . . where k_(j)=2π/λ_(j), p is the number of multiple passesthrough the at least one of said first and second measurement legs, andn_(j) are the refractive indices of gas in said at least one of saidmeasurement legs occupied by the gas corresponding to wavelength, λ_(j),and ζ_(j) are phase offsets not associated with optical paths andwherein said electronic means is further configured and arranged tocreate phases θ and Φ where${\vartheta = ( {{\frac{l_{1}}{p}\phi_{1}} + {\frac{l_{2}}{p}\phi_{2}}} )},{{{and}\quad \Phi} = ( {{\frac{l_{1}}{p}\phi_{1}} - {\frac{l_{2}}{p}\phi_{2}}} )}$

where l₁ and l₂ are non-integer values.
 6. The interferometric method ofclaim 5 wherein the refractivity of the gas, (n₁−1) is calculated usingthe formula:${{n_{1} - 1} = {\frac{\Gamma}{\chi \quad {L\lbrack {1 - ( {K/\chi} )^{2}} \rbrack}}\{ {\lbrack {{\vartheta ( {K/\chi} )} - \Phi} \rbrack - Q} \}}},$

where χ=(l₁k₁+l₂k₂)/2, K=(l₁k₁−l₂k₂)/2 and${\Gamma = \frac{n_{2} - 1}{n_{2} - n_{1}}},$

the quantity Γ being the reciprocal dispersive power of the gas which issubstantially independent of environmental conditions and turbulence inthe gas and the offset terms Q and ζ_(i) are defined as Q=ξ(K/χ)−Z where${\xi = ( {{\frac{l_{1}}{p}\zeta_{1}} + {\frac{l_{2}}{p}\zeta_{2}}} )},{Z = ( {{\frac{l_{1}}{p}\zeta_{1}} - {\frac{l_{2}}{p}\zeta_{2}}} )}$

with ξ and Z being determinable quantities.
 7. The interferometricmethod of claim 6 wherein said step of electronically analyzing isfurther performs calculating a physical distance, L, independent of theeffects of the refractive index of the gas in the measurement path usingthe formula$L = {\frac{1}{( {\chi + K} )}\{ {{\frac{l_{1}}{p}( {\phi_{1} - \zeta_{1}} )} - {\frac{\Gamma}{\lbrack {1 - ( {K/\chi} )} \rbrack}\lbrack {{( {K/\chi} )\vartheta} - \Phi - Q} \rbrack}} \}}$

where the ratio of the wavelengths can be expressed in terms of (K/χ)with$\frac{\lambda_{1}}{\lambda_{2}} = {{( \frac{l_{1}}{l_{2}} )\lbrack \frac{1 - ( {K/\chi} )}{1 + ( {K/\chi} )} \rbrack}.}$


8. The interferometric method of claim 5 wherein said step ofelectronically analyzing further compensates for differences in groupdelay experienced by said electrical interference signals.